From: imsconformance@imsglobal.org Sent: Tuesday, January 28, 2020 12:45 PM To: conformance@imsglobal.org Cc: hugh.rutledge@pearson.com Subject: Conformance Report Full Name: HughRutledge Email Address: hugh.rutledge@pearson.com Organization: Pearson Product Name: enVisionmath2.0 Grade 4 2017 Product Version: 1 Source: IMS Online Validator Profile: 1.2.0 Identifier: realize-2483526c-f65c-300c-a6ad-2b2cbb25758d Timestamp: Tuesday, January 28, 2020 12:43 PM EST Status: VALID! Conformant: true ----- VALID! ----- Resource Validation Results The document is valid. ----- VALID! ----- Schema Location Results Schema locations are valid. ----- VALID! ----- Schema Validation Results The document is valid. ----- VALID! ----- Schematron Validation Results The document is valid. Curriculum Standards: Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. - 4.N.2.8 Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. - 4.N.2.7 Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. - 4.N.2.6 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. - M.2.3 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. - M.2.4 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). - M.2.1 Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. - M.2.2 Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. - 1.3.1.1 Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. - 4.1.2.6 Read and write numbers to 1000 using base-ten numerals, number names and expanded form. - M.2.7 Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. - 4.1.2.5 Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, = and < symbols to record the results of comparisons. - M.2.8 Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. - 1.3.1.2 Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. - 4.1.2.4 Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). Understand the following as special cases: - M.2.5 Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. - 4.1.2.3 Count within 1000 and skip-count by 5s, 10s and 100s. - M.2.6 Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. - M.2.9 Round decimals to the nearest tenth. - 4.1.2.7 Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids. - NC.3.G.1.b Name shapes as flat or solid. - K.G.1 Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. - 5.DS.A.2 Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. - 5.DS.A.1 Demonstrate the ability to measure length or distance using objects. - 1.GM.B.7 Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. - NC.3.G.1.a Analyze and compare 2.D shapes. - K.G.8 Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. - NC.2.NBT.5.a Comparing addition and subtraction strategies, and explaining why they work. - NC.2.NBT.5.b Selecting an appropriate strategy in order to efficiently compute sums and differences. - NC.2.NBT.5.c Describe positions of shapes in the environment. - K.G.7 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. - NC.4.MD.3.c Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. - NC.4.MD.3.b Find areas of rectilinear figures with known side lengths. - NC.4.MD.3.a Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. - 5.NF.B.8 Analyze patterns and graph ordered pairs generated from number sequences. - 5.OA.8 Extend the concept of multiplication to multiply a fraction or whole number by a fraction. - 5.NF.B.7 Use tables to identify relationships between patterns. - 5.OA.7 Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. - 5.NF.B.6 Justify the reasonableness of a product when multiplying with fractions. - 5.NF.B.5 Compare the lengths of two objects indirectly by using a third object. - 1.GM.B.6 Estimate results of sums, differences and products with fractions and decimals to the thousandths. - 5.NF.B.4 Interpret numerical expressions without evaluating them. - 5.OA.4 Write simple expressions that show calculations with numbers. - 5.OA.3 Order three or more objects by length. - 1.GM.B.5 Analyze numerical patterns. - 5.OA.6 Understand two-digit numbers are composed of ten(s) and one(s). - 1.NBT.A.2 Compare two two-digit numbers using the symbols >, = or <. - 1.NBT.A.3 Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. - 5.GM.2.1 Evaluate expressions with parentheses, brackets, and braces. - 5.OA.2 Use the order of operations to evaluate expressions. - 5.OA.1 Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”. - 1.NBT.A.1 Count by 10s to 120 starting at any number. - 1.NBT.A.4 Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). - 4.N.2.1 Represent tenths and hundredths with concrete models, making connections between fractions and decimals. - 4.N.2.5 Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. - 4.N.2.4 Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). - 4.N.2.3 Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. - 4.N.2.2 Use patterns to add numbers together. - K.OA.9 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. - NC.2.NBT.1 Count within 1000; skip-count by 5s, 10s, and 100s. - NC.2.NBT.2 Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. - NC.2.NBT.3 Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. - NC.2.NBT.4 Add up to three two-digit numbers using strategies based on place value and properties of operations. - NC.2.NBT.6 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. - NC.2.NBT.8 Add up to four two-digit numbers using strategies based on place value and properties of operations. - M.2.10 Convert metric units of length. - 5.MD.10 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. - M.2.11 Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number 100-900. - M.2.12 Convert metric units of mass. - 5.MD.12 Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. - M.2.13 Convert metric units of capacity. - 5.MD.11 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. - M.2.18 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2… and represent whole-number sums and differences within 100 on a number line diagram. - M.2.19 Solve problems using data in a line plot. - 5.MD.17 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. - M.2.14 Define a first quadrant Cartesian coordinate system. - 5.GM.C.6 Measure the length of an object twice, using length units of different lengths for the two measurements, describe how the two measurements relate to the size of the unit chosen. - M.2.15 Solve real-world problems with measurement conversions. - 5.MD.13 Plot and interpret points in the first quadrant of the Cartesian coordinate plane. - 5.GM.C.7 Estimate lengths using units of inches, feet, centimeters, and meters. - M.2.16 Organize and display data in a line plot. - 5.MD.16 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. - M.2.17 Read and analyze line plots. - 5.MD.15 Show numbers in many ways. - K.OA.1 Represent addition as adding to a number. - K.OA.2 Determine if a set of objects has an odd or even number of members. - 2.RA.B.2 Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. - 2.RA.B.3 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). - M.2.21 Tell time to the hour and half-hour (analog and digital). - 1.GM.3.1 Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. - M.2.22 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. - M.2.23 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. - M.2.24 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. - M.2.20 Measure distances around objects. - 3.3.2.3 Find the perimeter of a polygon by adding the lengths of the sides. - 3.3.2.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. - M.2.25 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. - M.2.26 Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g., 425 > 276, 73 < 107, page 351 comes after page 350, 753 is between 700 and 800). - 2.N.1.6 Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three- digit number. - 2.N.1.4 Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds. - 2.N.1.3 Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. - 2.N.1.1 Building and drawing triangles, rectangles, squares, hexagons, circles. - NC.K.G.5.a Building cubes, cones, spheres, and cylinders. - NC.K.G.5.b Represent problems using equations with a letter standing for the unknown quantity. - NC.4.OA.3.c Interpret remainders in word problems. - NC.4.OA.3.b Use estimation strategies to assess reasonableness of answers. - NC.4.OA.3.a Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. - 1.2.1.1 Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units. - NC.3.MD.2.c Use math to explain what you know about counting. - K.NCC.11 Estimate and measure lengths in customary units to the quarter-inch and half-inch, and feet and yards to the whole unit. - NC.3.MD.2.a Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds. - NC.3.MD.2.b Compare groups by counting. - K.NCC.15 Count to the numbers 6 and 7. - K.NCC.18 Read and write the numbers 6 and 7. - K.NCC.19 Compose and decompose numbers from 11 to 19 into sets of tens with additional ones. - K.NBT.A.1 Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. - NC.5.NBT.3.b Write decimals using base-ten numerals, number names, and expanded form. - NC.5.NBT.3.a Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. - 1.A.1.1 Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: - NC.4.NF.2 Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. - NC.4.NF.1 Solve word problems by drawing pictures and writing equations. - 1.OA.17 Use addition facts to 10 to solve subtraction problems. - 1.OA.16 Use the same addends to write two different equations with the same sum. - 1.OA.14 Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. - 3.A.2.2 Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. - 3.A.2.1 Construct viable arguments and critique the reasoning of others. - K.MP.3 Generate two numerical patterns using two given rules. - NC.5.OA.3 Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: - NC.5.OA.2 Memorize doubles facts. - 1.OA.21 Count on to add using an open number line. - 1.OA.20 Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. - NC.4.NF.7 Use decimal notation to represent fractions. - NC.4.NF.6 Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. - NC.4.NF.3 Analyze and describe the properties of prisms and pyramids. - 5.GM.A.3 Classify figures in a hierarchy based on properties. - 5.GM.A.2 Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. - 4.A.2.1 Understand that attributes belonging to a category of figures also belong to all subcategories. - 5.GM.A.1 Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. - 4.A.2.2 Use estimation strategies to assess reasonableness of answers. - NC.3.NBT.2.a Critique the reasoning of others by using known information about addition and subtraction. - 1.OA.27 Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. - NC.3.NBT.2.b Use different ways to solve two-step problems. - 2.OA.19 Use expanded form to decompose numbers and then find sums and differences. - NC.3.NBT.2.c Use doubles facts to solve doubles-plus-2 facts. - 1.OA.23 Model problems using equations with unknowns in any position. - 2.OA.16 The student will sort and classify concrete objects according to one or two attributes. - 1.13 Model problems using equations, drawings, arrays, and bar diagrams. - 2.OA.15 Model and solve two-step problems using equations. - 2.OA.18 The student will use nonstandard units to measure and compare length, weight, and volume. - 1.10 Use drawings and equations to make sense of the words in problems. - 2.OA.17 Use different ways to tell if a group of objects shows an even or odd number. - 2.OA.12 Tell if a group of objects is even or odd. - 2.OA.11 Make arrays with equal rows or equal columns to solve addition problems. - 2.OA.14 Find the total number of objects in a set of rows and columns. - 2.OA.13 Use addition facts to find subtraction facts. - 1.OA.32 The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. - 4.7 Use half units when measuring distances. - 3.3.2.1 Use words to compare objects according to length, size, weight and position. - K.3.2.1 Decompose a rectangle into smaller rectangles to find the area of the original rectangle. - 3.GM.C.14 Find rectangular arrangements that can be formed for a given area. - 3.GM.C.13 Multiply whole-number side lengths to solve problems involving the area of rectangles. - 3.GM.C.12 Making a two-dimensional composite shape using rectangles, squares, trapezoids, triangles, and half- circles naming the components of the new shape. - NC.1.G.2.a Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value. - 3.GM.C.11 Making a three-dimensional composite shape using cubes, rectangular prisms, cones, and cylinders, naming the components of the new shape. - NC.1.G.2.b Label area measurements with squared units. - 3.GM.C.10 Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. - 2.N.3.2 100 can be thought of as a bundle of ten tens – called a “hundred.” - M.2.5a Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. - 2.N.3.1 Numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight or nine hundreds, and 0 tens and 0 ones. - M.2.5b Order 2 or 3 objects using measurable attributes, such as length and weight. - K.3.2.2 Properties of operations - NC.1.NBT.6.d The relationship between addition and subtraction - NC.1.NBT.6.e The student will demonstrate an understanding of equality through the use of the equal symbol. - 1.15 Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. - M.4.13 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. - M.4.12 Unitize by making a hundred from a collection of ten tens. - NC.2.NBT.1.a Concrete models and drawings - NC.1.NBT.6.a Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. - M.4.11 Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds, with 0 tens and 0 ones. - NC.2.NBT.1.b Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. - M.4.10 Compose and decompose numbers using various groupings of hundreds, tens, and ones. - NC.2.NBT.1.c Strategies based on place value - NC.1.NBT.6.c Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). - M.4.17 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. - M.4.16 Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) - M.4.19 The student will count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110. - 1.1d Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. - M.4.18 Generate measurement data to the nearest whole unit, and display the data in a line plot. - 2.DS.A.2 Draw a picture graph or a bar graph to represent a data set with up to four categories. - 2.DS.A.3 Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers. - 2.DS.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or sides. - 2.GM.A.1 Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares. - 2.GM.A.2 Solve problems using information presented in line plots, picture graphs and bar graphs. - 2.DS.A.4 Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole. - 2.GM.A.3 Draw conclusions from line plots, picture graphs and bar graphs. - 2.DS.A.5 Generate two numeric patterns given two rules. - 5.RA.A.1a Graph numeric patterns on the Cartesian coordinate plane. - 5.RA.A.1c Translate two numeric patterns into two sets of ordered pairs. - 5.RA.A.1b Identify the relationship between two numeric patterns. - 5.RA.A.1d Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. - M.4.24 The student will write the numerals 0 to 110 in sequence and out-of-sequence. - 1.1b Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: - M.4.23 Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. - M.4.26 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). - M.4.25 The student will count forward orally by ones to 110, starting at any number between 0 and 110. - 1.1a Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. - M.4.20 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). - M.4.22 Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) - M.4.21 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. - M.4.28 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. - M.4.27 Use the relationship between addition and subtraction to solve problems. - 2.NBT.B.9 Add or subtract within 1000, and justify the solution. - 2.NBT.B.8 Add up to four two-digit numbers. - 2.NBT.B.7 Demonstrate fluency with addition and subtraction within 100. - 2.NBT.B.6 Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. - 2.GM.C.8 Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line. - 2.GM.C.9 The student, given up to 110 objects, will order three or fewer sets from least to greatest and greatest to least. - 1.2c The student, given up to 110 objects, will group a collection into tens and ones and write the corresponding numeral. - 1.2a The student, given up to 110 objects, will compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to. - 1.2b Compose simple shapes to form larger shapes using manipulatives. - K.GM.C.10 Partition a regular polygon using physical models and recognize when those parts are equal. - 1.N.3.1 Interpret quotients of whole numbers. - 3.RA.A.2 Interpret products of whole numbers. - 3.RA.A.1 Use multiplication and division within 100 to solve problems. - 3.RA.A.4 Describe in words or drawings a problem that illustrates a multiplication or division situation. - 3.RA.A.3 Determine the unknown number in a multiplication or division equation relating three whole numbers. - 3.RA.A.5 Explain that equal shares of identical wholes need not have the same shape. - NC.2.G.3.c The student will tell time and write time to the nearest five minutes, using analog and digital clocks. - 2.9 Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. - 2.GM.2.1 Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. - 2.GM.2.2 Describe the shares using the words halves, thirds, half of, a third of, fourths, fourth of, quarter of. - NC.2.G.3.a Describe the whole as two halves, three thirds, four fourths. - NC.2.G.3.b Choose and use any strategy to add two-digit numbers. - 2.NC.7 Use drawings and equations to solve one-step and two-step problems. - 2.NC.8 Break apart numbers into tens and ones to find their sum. - 2.NC.5 Break apart addends and combine them in different ways to make numbers that are easy to add mentally. - 2.NC.6 Use an open number line to add tens and ones within 100. - 2.NC.3 Add within 100 using place-value strategies. - 2.NC.4 Add within 100 using place-value strategies and a hundred chart. - 2.NC.1 Add tens to two-digit numbers using an open number line. - 2.NC.2 A two-digit number and a one-digit number - NC.1.NBT.4.a A two-digit number and a multiple of 10 - NC.1.NBT.4.b The student will represent and solve practical problems involving equal sharing with two or four sharers. - 1.4a The student will represent and name fractions for halves and fourths, using models. - 1.4b Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. - NC.5.NBT.7.b Add and subtract decimals to thousandths using models, drawings or strategies based on place value. - NC.5.NBT.7.a Use estimation strategies to assess reasonableness of answers. - NC.5.NBT.7.d Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. - NC.5.NBT.7.c Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. - 5.GM.B.4b Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. - 5.GM.B.4a Add and subtract whole numbers up to and including 1,000. - NC.3.NBT.2 Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. - NC.3.NBT.3 The student, given a familiar problem situation involving magnitude, will select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, 500). - 1.5a Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. - NC.5.G.1 Classify quadrilaterals into categories based on their properties. - NC.5.G.3 Parentheses, using the order of operations. - NC.5.OA.2.a Commutative, associative and distributive properties. - NC.5.OA.2.b The student will create equations to represent equivalent mathematical relationships. - 3.17 Counting to 100 by ones. - NC.K.CC.1.a Counting to 100 by tens. - NC.K.CC.1.b Use data shown in a line plot to answer questions. - 3.DS.A.4 Create a line plot to represent data. - 3.DS.A.3 Solve one- and two-step problems using information presented in bar and/or picture graphs. - 3.DS.A.2 Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. - 3.DS.A.1 The student will recognize and describe with fluency part-whole relationships for numbers up to 10. - 1.7a Demonstrate fluency with products within 100. - 3.RA.C.8 Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. - 3.RA.C.7 Compose and decompose larger shapes using smaller two-dimensional shapes. - 1.GM.1.2 Recognize and combine groups with totals up to 5 (conceptual subitizing). - NC.K.OA.6 Demonstrate fluency with addition and subtraction within 5. - NC.K.OA.5 Identify trapezoids and hexagons by pointing to the shape when given the name. - 1.GM.1.1 For any number from 0 to 10, find the number that makes 10 when added to the given number using objects or drawings, and record the answer with a drawing or expression. - NC.K.OA.4 The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. - 3.1b Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings, and record each decomposition by a drawing or expression. - NC.K.OA.3 Represent addition and subtraction, within 10: - NC.K.OA.1 The student will demonstrate fluency with addition and subtraction within 10. - 1.7b Find the measure of an angle that turns through a fraction of a circle. - 4.MD.13 Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. - 5.2.1.1 Recognize and draw lines, rays, and angles with different measures. - 4.MD.12 Add to/Take from- Change Unknown - NC.2.OA.1.b.1 Be precise when solving measurement problems. - 4.MD.11 Add to/Take from- Change Unknown - NC.2.OA.1.b.2 Find the unknown length or width of a rectangle using the known area or perimeter. - 4.MD.10 Read and write numerals, and represent a number of objects with a written numeral, to 100. - NC.1.NBT.7 Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. - NC.2.MD.1 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. - NC.1.NBT.5 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. - NC.2.MD.7 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points and represent whole-number sums and differences, within 100, on a number line. - NC.2.MD.6 Write equations to show the parts of 8 and 9. - K.OA.24 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. - M.4.23a Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. - NC.2.MD.3 Understand that the two digits of a two-digit number represent amounts of tens and ones. - NC.1.NBT.2 Write equations to show the parts of 10. - K.OA.25 Compare two two-digit numbers based on the value of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. - NC.1.NBT.3 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. - NC.2.MD.2 Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. - NC.2.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. - M.4.23b Find number partners for 10. - K.OA.27 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. - NC.2.MD.4 Count to 150, starting at any number less than 150. - NC.1.NBT.1 One-Step problems: - NC.2.OA.1.a Unitize by making a ten from a collection of ten ones. - NC.1.NBT.2.a Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. - 2.3.3.2 Two-Step problems involving single digits: - NC.2.OA.1.b Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. - NC.1.NBT.2.b The student will compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ?), with models. - 3.2c Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens, with 0 ones. - NC.1.NBT.2.c The student will represent fractions and mixed numbers with models and symbols. - 3.2b The student will name and write fractions and mixed numbers represented by a model. - 3.2a Solve related addition and subtraction equations. - K.OA.20 Estimate measures and use a ruler to measure length and height to the nearest inch. - 2.MD.9 When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. - M.K.4a Tell time and use reasoning to state if the event is happening in the a.m. or p.m. - 2.MD.7 Understand that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted. - M.K.4b Estimate the length of an object by relating the length of the object to a measurement I know. - 2.MD.8 Understand that each successive number name refers to a quantity that is one larger. - M.K.4c Tell time to the nearest five minutes. - 2.MD.5 Say the time in different ways. - 2.MD.6 Solve problems with dollar bills. - 2.MD.3 Solve problems involving addition and subtraction of minutes. - 3.GM.B.6 Solve problems with coins. - 2.MD.1 Estimate time intervals in minutes. - 3.GM.B.5 Solve problems with dollar bills and coins that model 100 cents. - 2.MD.2 Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. - 3.GM.B.8 Measure or estimate length, liquid volume and weight of objects. - 3.GM.B.7 Tell and write time to the nearest minute. - 3.GM.B.4 Construct viable arguments and critique the reasoning of others. - 3.MP.3 Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. - 4.RA.A.3 Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. - 4.RA.A.2 The student will investigate the passage of time and tell time to the hour and half-hour, using analog and digital clocks. - 1.9a Use appropriate tools, such as a protractor and ruler, to solve problems. - 4.MD.17 Use addition and subtraction to solve problems with unknown angle measures. - 4.MD.16 The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. - 3.3b Use a protractor to measure and draw angles. - 4.MD.15 The student will estimate and determine the sum or difference of two whole numbers. - 3.3a Use known angle measures to measure unknown angles. - 4.MD.14 Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. - M.5.6b Use sharing to separate equal groups and to think about division. - 3.OA.5 Use repeated subtraction to show the relationship between division and subtraction. - 3.OA.6 Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base- ten numerals, number names and expanded form (e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)). - M.5.6a Gain fluency in multiplication when using 2and 5 as factors. - 3.OA.8 Use repeated addition to show the relationship between multiplication and addition. - 3.OA.1 Use number lines to join equal groups. - 3.OA.2 Use arrays as one way to think about and understand multiplication. - 3.OA.3 Understand and use the Commutative Property of Multiplication. - 3.OA.4 Build 2.D shapes that match given attributes. - K.G.13 Use materials to build 3.D shapes. - K.G.14 Gain fluency in multiplication when using 9 as a factor. - 3.OA.9 Analyze and compare 2.D and 3.D shapes. - K.G.10 Demonstrate an understanding of concepts of time and devices that measure time. - K.GM.B.3 Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. - 5.N.2.3 Identify pennies, nickels, dimes and quarters. - K.GM.B.5 Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. - 5.N.2.4 Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. - NC.4.G.2 Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. - 5.N.2.1 Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. - NC.4.G.3 Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. - 5.N.2.2 Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. - NC.4.G.1 Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. - NC.4.NF.4.a The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. - 3.4d Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems. - 5.A.1.1 Solve word problems involving multiplication of a fraction by a whole number. - NC.4.NF.4.b The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. - 3.4c Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates. - 5.A.1.2 The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. - 3.4b The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. - 3.4a Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably. - K.GM.1.3 Compose free-form shapes with blocks. - K.GM.1.5 Use smaller shapes to form a larger shape when there is an outline to follow. - K.GM.1.4 Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area and can be used to measure area. - M.3.20a Demonstrate fluency with addition and subtraction within 10. - 1.RA.C.8 Add and subtract within 20. - 1.RA.C.7 Tell time to the quarter-hour and distinguish between a.m. and p.m. - 2.3.3.1 Use basic shapes and spatial reasoning to represent objects in the real world. - K.GM.1.6 Recognize area as an attribute of plane figures and understand concepts of area measurement. A plane figure which can be covered without gaps or overlaps by b unit squares is said to have an area of b square units. - M.3.20b Compose and decompose numbers up to 10 with objects and pictures. - K.1.2.2 Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. - K.1.2.1 Evaluate expressions and solve equations involving variables when values for the variables are given. - 5.2.3.3 Recognize squares, circles, triangles, and rectangles. - K.GM.1.1 Make sense of problems and persevere in solving them. - MP.1 Reason abstractly and quantitatively. - MP.2 The student will sort and classify objects according to one attribute. - K.12 Look for and make use of structure. - MP.7 Look for and express regularity in repeated reasoning. - MP.8 Construct viable arguments and critique the reasoning of others. - MP.3 Model with mathematics. - MP.4 Use appropriate tools strategically. - MP.5 Attend to precision. - MP.6 The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. - 5.18 Express the length of an object as a whole number of non-standard length units. - NC.1.MD.2.a Describe the numerator as representing the number of pieces being considered. - 3.NF.A.2a Measure by laying multiple copies of a shorter object (the length unit) end to end (iterating) with no gaps or overlaps. - NC.1.MD.2.b Convert customary units of length. - 5.MD.7 Convert Customary Units of weight. - 5.MD.9 Convert customary units of capacity. - 5.MD.8 Find the volume of prisms in different ways. - 5.MD.3 Round whole numbers to the nearest 10 or 100. - 3.NBT.A.1 Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. - NC.5.NF.1 Find the volume of rectangular prisms using a formula. - 5.MD.2 Use models, prior knowledge of volumes, and previously learned strategies to solve word problems involving volume. - 5.MD.5 Use fractions to model and solve division problems. - NC.5.NF.3 Find the volume of a solid figure that is the combination of two or more rectangular prisms. - 5.MD.4 Multiply whole numbers by multiples of 10 in the range 10-90. - 3.NBT.A.4 Demonstrate fluency with addition and subtraction within 1000. - 3.NBT.A.3 Find the volume of solid figures. - 5.MD.1 Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. - 3.NBT.A.2 Describe the denominator as the number of pieces that make the whole. - 3.NF.A.2b The student will estimate and use U.S. Customary and metric units to measure liquid volume in cups, pints, quarts, gallons, and liters. - 3.7b The student will estimate and use U.S. Customary and metric units to measure length to the nearest ½ inch, inch, foot, yard, centimeter, and meter. - 3.7a Use words or mathematical symbols to express a rule for a given pattern. - 4.RA.C.7 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. - NC.5.NF.4 Generate a number pattern that follows a given rule. - 4.RA.C.6 Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Recognize volume as additive and find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems. - M.5.22c Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. - NC.5.NF.7 Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems. - M.5.22b Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes (e.g., to represent the associative property of multiplication). - M.5.22a Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. - 3.RA.D.10 Estimate and measure the length and height of objects in inches, feet, and yards. - 2.MD.11 Estimate measures and use tools to measure the length and height of objects to the nearest inch, foot, and yard. - 2.MD.10 Multiply or divide to solve problems involving a multiplicative comparison. - 4.RA.A.1 Tell how much longer one object is than another. - 2.MD.15 Measure the length and height of objects using different metric units. - 2.MD.14 Estimate measures and use a ruler, meter stick, or tape measure to measure length and height to the nearest centimeter or meter. - 2.MD.13 Estimate measures and use a ruler to measure length and height to the nearest centimeter. - 2.MD.12 The student, given no more than three sets, each set containing 10 or fewer concrete objects, will compare and describe one set as having more, fewer, or the same number of objects as the other set(s). - K.2a The student will represent and identify equivalencies among fractions and decimals, with and without models. - 5.2a The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. - 5.2b Given a number from 1–20, count out that many objects. - NC.K.CC.5.a The student will estimate and count the number of square units needed to cover a given surface in order to determine its area. - 3.8b The student will estimate and measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units. - 3.8a Given up to 20 objects, name the next successive number when an object is added, recognizing the quantity is one more/greater. - NC.K.CC.5.b Reason with two-dimensional shapes and their attributes. - NC.3.G.1 Reasoning about their size and using area and length models. - NC.4.NF.2.a Using benchmark fractions 0, ½, and a whole. - NC.4.NF.2.b Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. - NC.K.CC.5.c Comparing common numerator or common denominators. - NC.4.NF.2.c Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. - 3.N.2.8 Recognize the relationship between multiplication and division to represent and solve real-world problems. - 3.N.2.7 Given 10 objects in a scattered arrangement, identify how many. - NC.K.CC.5.d Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. - 3.N.2.4 Recognize that a number can be used to represent how many objects are in a set up to 10. - K.N.1.2 Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. - 3.N.2.3 Count aloud forward in sequence to 100 by 1’s and 10’s. - K.N.1.1 Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. - 3.N.2.6 Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. - 3.N.2.5 Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent. - 4.3.3.4 Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. - 2.3.1.2 Apply rotations (turns) of 90° clockwise or counterclockwise. - 4.3.3.3 Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. - 4.3.3.2 Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives. - K.N.1.6 Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, or expressions. - NC.K.OA.1.a Count forward, with and without objects, from any given number up to 10. - K.N.1.5 Demonstrate fluency of multiplication facts with factors up to 10. - 3.N.2.2 Apply translations (slides) to figures. - 4.3.3.1 Demonstrate understanding of addition and subtraction by making connections among representations. - NC.K.OA.1.b Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. - 3.N.2.1 Measure the lengths of objects and make a line plot to organize the data. - 2.MD.22 Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line. - 3.NF.A.4 Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. - 3.NF.A.5 Compare two fractions with the same numerator or denominator using the symbols >, = or <, and justify the solution. - 3.NF.A.6 Add and subtract on a number line. - 2.MD.20 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. - 1.RA.A.4 Explain why fraction comparisons are only valid when the two fractions refer to the same whole. - 3.NF.A.7 Using the words more than, less than or equal to compare and order whole numbers, with and without objects, from 0 to 10. - K.N.1.8 Represent, create, describe, complete, and extend growing and shrinking patterns with quantity and numbers in a variety of real-world and mathematical contexts. - 2.A.1.1 Identify quadrilaterals and use attributes to describe them. - 3.G.1 Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. - 1.RA.A.3 Solve problems that call for addition of three whole numbers whose sum is within 20. - 1.RA.A.2 Use addition and subtraction within 20 to solve problems. - 1.RA.A.1 Draw conclusions for graphs. - 2.MD.25 Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. - 3.NF.A.1 Draw picture graphs and use them to solve problems. - 2.MD.24 Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole. - 3.NF.A.2 Draw bar graphs and use them to solve problems. - 2.MD.23 Represent fractions on a number line. - 3.NF.A.3 Add and subtract to solve measurement problems by using drawings and equations. - 2.MD.19 The student will tell how many are in a given set of 20 or fewer objects by counting orally. - K.1a Add or subtract to solve problems about measurements. - 2.MD.18 Solve problems by adding or subtracting length measurements. - 2.MD.17 The student will solve practical problems related to elapsed time in one-hour increments within a 12- hour period. - 3.9b Classify shapes according to their attributes. - 3.G.2 The student will tell time to the nearest minute, using analog and digital clocks. - 3.9a Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. - 4.4.1.1 Analyze and compare quadrilaterals and group them by their attributes. - 3.G.3 The student will read, write, and represent numbers from 0 through 20. - K.1b Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object. - K.NS.B.5 Demonstrate that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted. - K.NS.B.6 Demonstrate that each successive number name refers to a quantity that is one larger than the previous number. - K.NS.B.7 Recognize, without counting, the quantity of groups up to 5 objects arranged in common patterns. - K.NS.B.8 Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools. - 3.GM.3.2 Demonstrate that a number can be used to represent “how many” are in a set. - K.NS.B.9 Skip count by tens to 100. - K.NCC.41 Count by tens and ones from any number up to 100. - K.NCC.44 Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category. - 2.D.1.1 Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s. - 2.D.1.2 Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares. - NC.3.MD.5 Represent and interpret scaled picture and bar graphs: - NC.3.MD.3 Add or subtract mentally 10 or 100 to or from a given number within 1000. - 2.NBT.B.10 Relate area to the operations of multiplication and addition. - NC.3.MD.7 Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. - NC.3.MD.8 Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. - NC.3.NF.3.c The student will recognize and describe with fluency part-whole relationships for numbers up to 5. - K.4a Explaining that a fraction with the same numerator and denominator equals one whole. - NC.3.NF.3.b The student will investigate and describe part-whole relationships for numbers up to 10. - K.4b Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. - NC.3.NF.3.a Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. - NC.3.MD.1 Solve problems involving customary measurement. - NC.3.MD.2 Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. - 4.3.1.1 Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data. - 5.4.1.2 Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one. - 2.D.1.3 Draw conclusions and make predictions from information in a graph. - 2.D.1.4 Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. - 4.GM.A.1 Classify two-dimensional shapes by their sides and/or angles. - 4.GM.A.2 Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. - 5.NBT.A.1 Reason abstractly and quantitatively. - PS.2 Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. - 1.1.1.1 Ask and answer questions about the total number of data points. - NC.1.MD.4.a Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. - 5.NBT.A.2 Make sense of problems and persevere in solving them. - PS.1 Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left. - 5.NBT.A.3 Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. - 1.1.1.2 Ask and answer questions about how many in each category. - NC.1.MD.4.b Count, with and without objects, forward and backward from any given number up to 120. - 1.1.1.3 Find a number that is 10 more or 10 less than a given number. - 1.1.1.4 Partition circles and rectangles into two, three, or four equal shares. - NC.2.G.3 Compare and order whole numbers up to 100. - 1.1.1.5 Recognize and draw triangles, quadrilaterals, pentagons, and hexagons, having specified attributes; recognize and describe attributes of rectangular prisms and cubes. - NC.2.G.1 Use words to describe the relative size of numbers. - 1.1.1.6 Look for and express regularity in repeated reasoning. - PS.8 Look for and make use of structure. - PS.7 Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. - NC.5.NBT.1.b Model with mathematics. - PS.4 Ask and answer questions about how many more or less are in one category than in another. - NC.1.MD.4.c Construct viable arguments and critique the reasoning of others. - PS.3 Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. - NC.5.NBT.1.a Construct lines of symmetry for a two-dimensional figure. - 4.GM.A.3 Attend to precision. - PS.6 Use appropriate tools strategically. - PS.5 Tell time to the half hour. - 1.MD.13 The student will count forward orally by ones from 0 to 100. - K.3a Choose an appropriate tool and use it to measure a given object. - 1.MD.10 Tell time to the hour. - 1.MD.11 The student will count forward by tens to determine the total number of objects to 100. - K.3d The student will estimate and determine the product and quotient of two numbers involving decimals. - 5.5a The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. - 5.5b Read and write numerals and represent a number of objects with a written numeral. - 1.NS.A.2 Understand the whole is partitioned into equal parts. - 3.NF.A.3b Count to the numbers 8 and 9. - K.NCC.20 Understand the whole is the interval from 0 to 1. - 3.NF.A.3a Count to 120, starting at any number less than 120. - 1.NS.A.1 Count backward from a given number between 20 and 1. - 1.NS.A.3 Show how to make a group of ten. - K.NCC.24 Understand a fraction represents the endpoint of the length a given number of partitions from 0. - 3.NF.A.3c Recording each composition or decomposition by a drawing or expression. - NC.K.NBT.1.b Using objects or drawings. - NC.K.NBT.1.a Understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. - NC.K.NBT.1.c Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. - 5.NBT.A.8 Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. - NC.3.OA.2.b Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. - 3.1.3.1 Understand that the size of a fractional part is relative to the size of the whole. - 3.1.3.2 Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. - NC.3.OA.2.a Evaluate the value of powers of 10 and understand the relationship to the place value system. - 5.NBT.A.4 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. - 5.6a Round numbers from billions to thousandths place. - 5.NBT.A.5 The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. - 5.6b Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. - 5.NBT.A.6 Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. - 5.NBT.A.7 Count and write numbers 11 and 12. - K.NCC.32 Count and write numbers 13, 14, and 15. - K.NCC.33 Count forward from any number to a number within 20. - K.NCC.36 Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. - 4.3.1.2 Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. - 4.NF.B.6 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. - 4.NF.B.7 Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams). - 1.D.1.1 Use patterns to count to 30. - K.NCC.39 Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. - 4.NF.B.4 Use data to create picture and bar-type graphs to demonstrate one-to-one correspondence. - 1.D.1.2 Find the volume of a rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths. - NC.5.MD.5.a Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. - 4.NF.B.5 Draw conclusions from picture and bar-type graphs. - 1.D.1.3 Find volume of solid figures with one-digit dimensions composed of two non-overlapping rectangular prisms. - NC.5.MD.5.c Build understanding of the volume formula for rectangular prisms with whole-number edge lengths in the context of solving problems. - NC.5.MD.5.b Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. - 2.2.1.1 Interpret organized data. - 1.MD.3 Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.1.1.4 Estimate solutions to arithmetic problems in order to assess the reasonableness of results. - 5.1.1.3 Order objects by length. - 1.MD.6 Solve problems involving multiplication of a fraction by a whole number. - 4.NF.B.8 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. - NC.K.MD.3 Use objects to measure length. - 1.MD.8 Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. - NC.4.OA.1 Describe measurable attributes of objects; and describe several different measurable attributes of a single object. - NC.K.MD.1 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. - NC.K.MD.2 Solve two-step word problems involving the four operations with whole numbers. - NC.4.OA.3 Generate and analyze a number or shape pattern that follows a given rule. - NC.4.OA.5 Organize data into categories. - 1.MD.1 Compare and order whole numbers up to 1000. - 2.1.1.5 Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. - 2.1.1.2 Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three- digit number. - 2.1.1.3 Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. - 2.1.1.1 Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. - 5.1.1.2 Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. - 5.1.1.1 Find better and faster ways to solve problems. - 1.NC.7 Count to 120 using an open number line. - 1.NC.5 Represent and identify unit fractions using area and length models. - NC.3.NF.1.b Explain that a unit fraction is one of those parts. - NC.3.NF.1.a Read and write numbers 11 to 19. - 1.NC.8 Show groups of 10 with connecting cubes. - 1.NC.9 Solve multi-step problems that require measurement conversions. - 5.GM.D.9 The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. - 5.8a Pairing objects, then counting them by 2s. - NC.2.OA.3.a Count by 1s to 120. - 1.NC.2 Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. - 3.D.1.2 Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. - 3.1.3.3 Determining whether objects can be placed into two equal groups. - NC.2.OA.3.b Relate area to the operations of multiplication and addition. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. - M.3.22c Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. - M.3.22b Writing an equation to express an even number as a sum of two equal addends. - NC.2.OA.3.c Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole- number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. - M.3.22a Convert measurements of capacity, length and weight within a given measurement system. - 5.GM.D.8 Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. - 4.2.1.1 Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. - 4.GM.C.7 Apply the area and perimeter formulas for rectangles to solve problems. - 4.GM.C.8 Know relative sizes of measurement units within one system of units. - 4.GM.C.6 Relate area to the operations of multiplication and addition. Recognize area as additive and find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. - M.3.22d Partition circles and rectangles into two and four equal shares. - NC.1.G.3 Write, evaluate and interpret numeric expressions using the order of operations. - 5.RA.B.3 Translate written expressions into algebraic expressions. - 5.RA.B.4 The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. - 5.9a The student will solve practical problems involving length, mass, and liquid volume using metric units. - 5.9b Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. - 3.D.1.1 Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. - 4.D.1.3 Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols. - M.5.1 Recognize shapes by how they look. - 1.G.1 Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. - 4.D.1.1 Describe plane shapes by how they look. - 1.G.2 Draw polygon shapes. - 1.G.3 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. - M.5.4 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. - M.5.5 Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.) - M.5.2 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. (e.g., Given the rule “Add 3” and the starting number 0 and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.) - M.5.3 Fluently multiply multi-digit whole numbers using the standard algorithm. - M.5.8 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - M.5.9 Use place value understanding to round decimals to any place. - M.5.7 Represent tenths and hundredths with models, making connections between fractions and decimals. - NC.4.NF.6.c Draw cubes and describe how they look. - 1.G.4 Use counting and comparison skills to create and analyze bar graphs and tally charts. - 1.1.1.7 Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks. - 3.1.1.1 Define 3-D shapes by their number of edges, vertices, and faces or flat surfaces. - 1.G.5 Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. - 3.1.1.2 Divide circles and rectangles into halves, thirds, and fourths. - 1.G.6 Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. - 3.1.1.4 Make equal shares that do not have the same shape. - 1.G.7 Use repeated reasoning to divide rectangles into rows and columns and to create designs with equal shares. - 1.G.8 Determine whether shapes are divided into equal shares. - 1.G.9 Express, model and explain the equivalence between fractions with denominators of 10 and 100. - NC.4.NF.6.a Use equivalent fractions to add two fractions with denominators of 10 or 100. - NC.4.NF.6.b Find combinations of coins that equal a given amount. - 2.GM.D.13 Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. - 2.GM.D.12 Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock. - 2.GM.D.11 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. - 2.GM.D.10 Create and analyze line and double-bar graphs with whole numbers, fractions, and decimals increments. - 5.D.1.2 Model addition and subtraction of fractions and decimals using a variety of representations. - 5.1.3.2 Measure angles in geometric figures and real-world objects with a protractor or angle ruler. - 4.GM.2.1 Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. - 5.1.3.1 Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. - 5.1.3.4 Estimate sums and differences of decimals and fractions to assess the reasonableness of results. - 5.1.3.3 Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric). - 4.GM.2.5 Find the area of polygons that can be decomposed into rectangles. - 4.GM.2.2 Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. - 5.2.1.2 Tell and write time in hours and half-hours using analog and digital clocks. - M.1.17 Look for and make use of structure. - 1.MP.7 Organize, represent, interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category and how many more or less are in one category than in another. - M.1.18 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, and/or overall size); build and draw shapes to possess defining attributes. - M.1.19 Look for and express regularity in repeated reasoning. - 1.MP.8 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count and explain the reasoning used. - M.1.13 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences) using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. - M.1.14 Order three objects by length and compare the lengths of two objects indirectly by using a third object. - M.1.15 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Instructional Note: Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. - M.1.16 Multiply a whole number by a fraction. - 5.NC.61 Add or subtract a multiple of 10 from another two-digit number, and justify the solution. - 1.NBT.B.7 Multiply two fractions. - 5.NC.65 Construct viable arguments and critique the reasoning of others. - 1.MP.3 Use models to multiply two fractions. - 5.NC.64 Use appropriate tools strategically. - 1.MP.5 Multiply fractions and whole numbers. - 5.NC.63 Multiply a fraction by a whole number. - 5.NC.62 Locate points on a coordinate grid. - 5.G.1 Graph points on a coordinate grid. - 5.G.2 Solve real-world problems by graphing points. - 5.G.3 Classify triangles by their angles and sides. - 5.G.5 Classify quadrilaterals by their properties. - 5.G.6 Add and subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.59 Classify quadrilaterals using a hierarchy. - 5.G.7 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter- circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape and compose new shapes from the composite shape. Instructional Note: Students do not need to learn formal names such as, “right rectangular prism.” - M.1.20 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares and understand for these examples that decomposing into more equal shares creates smaller shares. - M.1.21 Demonstrate that equal shares of identical wholes need not have the same shape. - 2.GM.A.3a Counting on - NC.1.OA.6.a Using a number line - NC.1.OA.6.e Using the relationship between addition and subtraction - NC.1.OA.6.d Decomposing a number leading to a ten - NC.1.OA.6.c Making ten - NC.1.OA.6.b Use multiplication to divide a whole number by a unit fraction. - 5.NC.72 Implement division of fractions to show quotients as fractions and mixed numbers. - 5.NC.71 Understand how fractions are related to division. - 5.NC.70 Creating equivalent but simpler or known sums - NC.1.OA.6.f Solve multi-step problems involving division with unit fractions. - 5.NC.76 Apply the formulas V = l × w × h and V = B × h for volume of right rectangular prisms with whole-number edge lengths. - 5.GM.B.5 Use models to divide whole numbers and unit fractions. Check your answer using multiplication. - 5.NC.75 Understand the concept of volume and recognize that volume is measured in cubic units. - 5.GM.B.4 Use models to divide unit fractions by non-zero whole numbers. - 5.NC.74 Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. - 5.NC.73 Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. - 3.4.1.1 Demonstrate fluency with addition and subtraction within 20. - 2.RA.A.1 Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. - 5.NC.68 Use models, equations, and previously learned strategies to multiply mixed numbers. - 5.NC.67 Find the area of a rectangle using fractions and diagrams. - 5.NC.66 Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. - 4.1.1.3 Use an understanding of place value to multiply a number by 10, 100 and 1000. - 4.1.1.2 Demonstrate fluency with multiplication and division facts. - 4.1.1.1 Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. - 4.OA.11 Illustrate that the length of an object is the number of same-size units of length that, when laid end-to- end with no gaps or overlaps, reach from one end of the object to the other. - 1.GM.2.2 Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. - 4.OA.12 Use nonstandard and standard measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement. - 1.GM.2.1 Write and solve two-step problems involving variables using any of the four operations. - 3.RA.D.9 Use multiplication to find multiples of a given number. - 4.OA.10 Generate a shape pattern that follows a given rule and predict a shape in the pattern. - 4.OA.13 Describe a length to the nearest whole unit using a number and a unit. - 1.GM.2.4 Solve problems by using patterns. - 4.OA.14 Measure the same object/distance with units of two different lengths and describe how and why the measurements differ. - 1.GM.2.3 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (e.g., describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8). - M.3.2 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). - M.3.3 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). - M.3.1 Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). - M.3.6 Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. - 4.1.1.6 Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. - M.3.7 Measure the length of an object in terms of multiple copies of another object. - 1.3.2.1 Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 4.1.1.5 Tell time to the hour and half-hour. - 1.3.2.2 Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 =?). - M.3.4 Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. - 4.1.1.4 Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. - M.3.5 Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). - M.3.8 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). - M.3.9 Know the value of a penny, nickel, dime and quarter. - 1.GM.C.9 Tell and write time in hours and half-hours using analog and digital clocks. - 1.GM.C.8 Understand that parts of a whole can be expressed as fractions and or decimals. - 5.NF.A.1 Collect and sort information about objects and events in the environment. - K.D.1.1 The student will collect, organize, and represent data in pictographs or bar graphs. - 3.15a The student will read and interpret data represented in pictographs and bar graphs. - 3.15b Draw conclusions from object graphs, picture graphs, T-charts and tallies. - 1.DS.A.2 Collect, organize and represent data with up to three categories. - 1.DS.A.1 Compare and order fractions and or decimals to the thousandths place using the symbols >, = or <, and justify the solution. - 5.NF.A.3 Convert decimals to fractions and fractions to decimals. - 5.NF.A.2 Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. - 4.MD.5 Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. - 4.MD.6 Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. - 4.MD.7 Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. - 4.MD.8 Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. - 4.MD.9 Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. - 4.N.1.2 Demonstrate fluency with multiplication and division facts with factors up to 12. - 4.N.1.1 Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). - 4.N.1.6 Read and interpret data using line plots. - 4.MD.1 Represent data using line plots and interpret data in line plots to solve problems. - 4.MD.2 Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. - 4.N.1.5 Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. - 5.GM.3.4 Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. - 4.N.1.4 Solve problems involving line plots and fractions. - 4.MD.3 Recognize and use the relationship between inches, feet, and yards to measure and compare objects. - 5.GM.3.3 Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. - 4.N.1.3 Critique the reasoning of others using an understanding of line plots. - 4.MD.4 The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight or nine tens (and 0 ones). - M.1.10c 10 can be thought of as a bundle of ten ones — called a “ten.” (e.g., A group of ten pennies is equivalent to a dime.) - M.1.10a The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight or nine ones. - M.1.10b Understand the relationship between numbers and quantities. - NC.K.CC.4 Count forward beginning from a given number within the known sequence, instead of having to begin at 1. - NC.K.CC.2 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. - NC.K.CC.3 Use models and strategies to solve word problems. - 5.NC.20 Identify whether the number of objects, within 10, in one group is greater than, less than, or equal to the number of objects in another group, by using matching and counting strategies. - NC.K.CC.6 Compare two numbers, within 10, presented as written numerals. - NC.K.CC.7 Add and subtract decimals. - 5.NC.13 Subtract decimals to the hundredths using the standard algorithm. - 5.NC.12 Add decimals to the hundredths using the standard algorithm. - 5.NC.11 Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. - 5.NC.18 Multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products. - 5.NC.17 Use rounding and compatible numbers to estimate products. - 5.NC.16 Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. - 5.NC.15 Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. - 5.NC.19 Create an input/output chart or table to represent or extend a numerical pattern. - 4.A.1.1 Create growth patterns involving geometric shapes and define the single operation rule of the pattern. - 4.A.1.3 Understand that rectangles can have equal perimeters but different areas, or rectangles can have equal areas but different perimeters. - 3.GM.D.16 Solve problems involving perimeters of polygons. - 3.GM.D.15 Use addition and subtraction to solve word problems. - 2.OA.9 Add and subtract quickly and accurately using mental math strategies. - 2.OA.8 Make a 10 to subtract quickly and accurately. - 2.OA.7 Think addition to subtract quickly and accurately. - 2.OA.6 Count on and count back on a number line to subtract. - 2.OA.5 Use number patterns on an addition facts table to complete related addition equations that show basic facts. - 2.OA.4 Use place-value patterns and mental math to find quotients. - 5.NC.32 Use the strategy of making a ten to add quickly and accurately. - 2.OA.3 Use doubles and near doubles to add quickly and accurately. - 2.OA.2 Multiply decimals using the standard algorithm for multiplication and multiplication strategies. - 5.NC.30 Use counting on to add numbers and add numbers in any order. - 2.OA.1 Use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole number. - 5.NC.25 Use models to represent multiplying a decimal and a whole number. - 5.NC.24 Use rounding and compatible numbers to estimate the product of a decimal and a whole number. - 5.NC.23 Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. - 5.NC.22 Use number sense and reasoning to place the decimal point in a product. - 5.NC.29 Use properties to multiply decimals. - 5.NC.28 Multiply decimals using partial products and models. - 5.NC.27 Use grids to model decimals and find the product of a decimal and a decimal. - 5.NC.26 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. - M.3.12 The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth. - 5.1 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. - M.3.11 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. - 5.4 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.13 The student will simplify whole number numerical expressions using the order of operations. - 5.7 Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. - 3.3.1.2 Use place value understanding to round whole numbers to the nearest 10 or 100. - M.3.10 Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. - 3.3.1.1 Know relationships among units of time. - 3.3.3.2 Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. - 3.3.3.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). - M.1.1 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves or quarters. - M.3.19 Find the perimeter of different polygons. - 3.MD.21 Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). - M.3.16 Understand subtraction as an unknown-addend problem (e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8). - M.1.4 Use the given sides of a polygon and the known perimeter to find the unknown side length. - 3.MD.23 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). - M.1.5 Find the perimeter of different polygons with common shapes. - 3.MD.22 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). - M.3.18 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). - M.1.2 Understand the relationship of shapes with the same area and different perimeters. - 3.MD.25 Apply properties of operations as strategies to add and subtract (e.g., If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known: Commutative Property of Addition. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12: Associative Property of Addition). Instructional Note: Students need not use formal terms for these properties. - M.1.3 Understand the relationship of shapes with the same perimeter and different areas. - 3.MD.24 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. Instructional Note: Exclude compound units such as cm3 and finding the geometric volume of a container. - M.3.17 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., Determine the unknown number that makes the equation true in each of the equations. 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?). - M.1.8 Use concrete models and structured arrangements, such as repeated addition, arrays and ten frames to develop understanding of multiplication. - 2.N.2.6 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. - M.1.9 Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. - 2.N.2.5 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). - M.1.6 Use strategies and algorithms based on knowledge of place value and equality to add and subtract two- digit numbers. - 2.N.2.4 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false (e.g., Which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2). - M.1.7 Use the standard algorithm for division to divide decimals by a whole number. - 5.NC.43 Demonstrate fluency with basic addition facts and related subtraction facts up to 20. - 2.N.2.2 Use models to help find quotients in problems involving decimals. - 5.NC.42 Use the relationship between addition and subtraction to generate basic facts up to 20. - 2.N.2.1 Use reason and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. - 5.NC.41 Use mental math and place-value patterns to divide a decimal by a power of 10. - 5.NC.40 Identify triangles, quadrilaterals, pentagons, hexagons, circles and cubes. - 2.GM.A.1a Round greater whole numbers to estimate sums and differences. - 4.NC.7 Find the quotient when the divisor is a multiple of 10. - 5.NC.36 Add numbers to one million with and without regrouping using the standard algorithm. - 4.NC.8 Solve division problems using partial quotients. - 5.NC.35 Use place value and an algorithm to subtract whole numbers. - 4.NC.9 Use models to find quotients. - 5.NC.34 Identify the faces of three-dimensional objects. - 2.GM.A.1b Use compatible numbers and place-value patterns to estimate quotients. - 5.NC.33 Use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors. - 5.NC.38 Decide where to place the first digit of the quotient when dividing whole numbers. - 5.NC.37 Determine whether a given whole number is a multiple of a given one-digit number. - NC.4.OA.4.b Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. - M.3.23 Use standard units to estimate liquid volume. - 3.MD.16 Recognize that a whole number is a multiple of each of its factors. - NC.4.OA.4.a Use addition or subtraction basic facts to represent a given problem situation using a number sentence. - 1.2.2.4 Solve word problems involving addition and subtraction to measure quantities of time. - 3.MD.15 Read and write numbers in expanded form, with numerals, and using number names. - 4.NC.1 Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. - 1.2.2.1 Use a pan balance with metric weights to measure the mass of objects in grams and kilograms. - 3.MD.18 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. - M.3.25 Recognize the relationship between adjacent digits in a multi-digit number. - 4.NC.2 Determine if equations involving addition and subtraction are true. - 1.2.2.2 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. - M.3.24 Use standard units to estimate the masses of solid objects. - 3.MD.17 Use place value to compare multi-digit numbers. - 4.NC.3 Use place value to round multi-digit numbers. - 4.NC.4 Use pictures to help solve problems about mass and volume. - 3.MD.19 Use previously learned concepts and skills to construct arguments about place value. - 4.NC.5 Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). - M.3.21 Add and subtract whole numbers mentally using a variety of methods. - 4.NC.6 Solve problems with area and perimeter. - NC.4.MD.3 Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. - NC.4.MD.2 Know relative sizes of measurement units. Solve problems involving metric measurement. - NC.4.MD.1 Determine whether a survey question will yield categorical or numerical data. - NC.4.MD.4.c Use scaled bar graphs to represent data sets. - 3.MD.10 Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. - NC.4.MD.4.b Collect data by asking a question that yields numerical data. - NC.4.MD.4.a Use graphs to solve problems. - 3.MD.11 Tell and write time to the nearest minute and measure time intervals in minutes. - 3.MD.14 Determine if the number is prime or composite. - NC.4.OA.4.c Show and tell time to the nearest minute using analog and digital clocks. - 3.MD.13 Find common denominators for fractions with unlike denominators. - 5.NC.50 Estimate sums and differences of fractions and mixed numbers. - 5.NC.54 Write equivalent fractions to add and subtract fractions with unlike denominators. - 5.NC.53 Subtract fractions with unlike denominators. - 5.NC.52 Add fractions with unlike denominators using equivalent fractions with a common denominator. - 5.NC.51 Use the standard algorithm to divide decimals, annexing zeros as needed. - 5.NC.47 Use the standard algorithm and place-value patterns to divide a decimal by another decimal. - 5.NC.46 Use number sense and reasoning to place the decimal point in the quotient when dividing two decimals. - 5.NC.45 Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts. - 5.GM.1.1 Use models to visualize the relationship between division and multiplication to divide decimals by a 2- digit whole number. - 5.NC.44 Estimate sums and differences of fractions by using the nearest half or whole number. - 5.NC.49 Solve word problems involving addition and subtraction of time intervals that cross the hour. - NC.4.MD.8 Develop an understanding of angles and angle measurement. - NC.4.MD.6 Represent and interpret data using whole numbers. - NC.4.MD.4 Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. - 4.N.3.1 The student will investigate and describe the concept of variable. - 5.19a The student will write an equation to represent a given mathematical relationship, using a variable. - 5.19b Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. - 3.A.1.1 Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. - 5.NF.B.7a Create a frequency table and/or line plot to display measurement data. - 4.DS.A.1 Calculate and interpret the product of two fractions less than one. - 5.NF.B.7c Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. - 5.NF.B.7b Look for and express regularity in repeated reasoning. - 2.MP.8 Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. - NC.4.NBT.5 Interpret a fraction as an equal sharing context, where a quantity is divided into equal parts. - NC.5.NF.3.a Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or - NC.4.NBT.6 Model and interpret a fraction as the division of the numerator by the denominator. - NC.5.NF.3.b Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. - NC.4.NBT.7 Count by 2s to 100 starting with any even number. - 2.RA.B.2a Model with mathematics. - 2.MP.4 Express even numbers as pairings or groups of 2, and write an expression to represent the number using addends of 2. - 2.RA.B.2b Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. - NC.4.NBT.1 Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. - NC.4.NBT.2 Solve one-step word problems involving division of whole numbers leading to answers in the form of fractions and mixed numbers, with denominators of 2, 3, 4, 5, 6, 8, 10, and 12, using area, length, and set models or equations. - NC.5.NF.3.c Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. - NC.4.NBT.4 Determine if equations involving addition and subtraction are true. - 1.N.2.2 Represent and solve real-world and mathematical problems using addition and subtraction up to ten. - 1.N.2.1 Demonstrate fluency with basic addition facts and related subtraction facts up to 10. - 1.N.2.3 Solve problems involving addition and subtraction by using information presented in a data display. - 4.DS.A.2 Analyze the data in a frequency table, line plot, bar graph or picture graph. - 4.DS.A.3 Recognize trapezoids and hexagons. - 2.GM.1.1 Describe, compare, and classify two-dimensional figures according to their geometric attributes. - 2.GM.1.2 Define the second number in an ordered pair as the vertical distance from the origin. - 5.GM.C.6d Use rounding or compatible numbers to estimate sums and differences. - 5.NC.9 Describe the whole as two of, or four of the shares. - NC.1.G.3.b Explain that decomposing into more equal shares creates smaller shares. - NC.1.G.3.c Use properties of addition and strategies to solve problems mentally. - 5.NC.8 Describe the shares as halves and fourths, as half of and fourth of. - NC.1.G.3.a Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. - NC.5.MD.1 Use place value to compare decimals through thousandths. - 5.NC.5 The student will identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms). - 2.13 Read and write decimals through thousandths in different ways. - 5.NC.4 Represent and interpret data. - NC.5.MD.2 Use a combination of coins to represent a given amount of money up to one dollar. - 2.N.4.2 Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. - NC.5.MD.4 Round decimals to different places. - 5.NC.6 Determine the value of a collection(s) of coins up to one dollar using the cent symbol. - 2.N.4.1 Use exponents to write powers of 10 and calculate products. - 5.NC.1 Represent the axes as scaled perpendicular number lines that both intersect at 0, the origin. - 5.GM.C.6a Identify any point on the Cartesian coordinate plane by its ordered pair coordinates. - 5.GM.C.6b Represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals. - 5.NC.3 Read and write whole numbers using standard form, expanded form, and number names. - 5.NC.2 Define the first number in an ordered pair as the horizontal distance from the origin. - 5.GM.C.6c Estimate the size of the product based on the size of the two factors. - 5.NF.B.5a Relate volume to the operations of multiplication and addition. - NC.5.MD.5 Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. - 5.NF.B.5c Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number. - 5.NF.B.5b Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1. - 5.NF.B.5d Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. - NC.4.MD.6.c Classify quadrilaterals by lines and angles. - 4.G.3 Apply understanding of the equal sign to determine if equations involving addition and subtraction are true. - NC.1.OA.7 Recognize and draw lines of symmetry. Identify line symmetric figures. - 4.G.4 Measure and sketch angles in whole-number degrees using a protractor. - NC.4.MD.6.b Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. - NC.4.MD.6.a Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. - NC.3.MD.3.b Draw and identify perpendicular, parallel, and intersecting lines. - 4.G.1 Demonstrate fluency with addition and subtraction within 10. - NC.1.OA.9 Classify triangles by line segments and angles. - 4.G.2 Solve one and two-step “how many more” and “how many less” problems using information from these graphs. - NC.3.MD.3.c Determine the unknown whole number in an addition or subtraction equation involving three whole numbers. - NC.1.OA.8 Express even numbers as being composed of equal groups and write an expression to represent the number with 2 equal addends. - 2.RA.B.2c Collect data by asking a question that yields data in up to four categories. - NC.3.MD.3.a Draw figures that have line symmetry. - 4.G.5 Identify arithmetic patterns and explain the patterns using properties of operations. - 3.RA.E.11 Use understanding of two-dimensional shapes to critique the reasoning of others. - 4.G.6 Measure the length of an object by selecting and using appropriate tools. - 2.GM.B.4 Analyze the results of measuring the same object with different units. - 2.GM.B.5 Estimate lengths using units of inches, feet, yards, centimeters and meters. - 2.GM.B.6 Measure to determine how much longer one object is than another. - 2.GM.B.7 Compare two three-digit numbers using the symbols >, = or <. - 2.NBT.A.5 Read and write numbers to 1000 using number names, base-ten numerals and expanded form. - 2.NBT.A.4 Count within 1000 by 1s, 10s and 100s starting with any number. - 2.NBT.A.3 Understand that 100 can be thought of as 10 tens – called a “hundred”. - 2.NBT.A.2 The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. - 2.17 Understand three-digit numbers are composed of hundreds, tens and ones. - 2.NBT.A.1 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units. - M.5.20b The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. - 2.16 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume. - M.5.20a Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. - M.5.16 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. (e.g., Interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?) - M.5.13 Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. - M.5.11 Apply the commutative and associative properties as strategies for solving addition problems. - NC.1.OA.3 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). - M.5.12 Represent and solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, by using objects, drawings, and equations with a symbol for the unknown number. - NC.1.OA.2 Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. - M.5.10 Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem. - NC.1.OA.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally). - M.5.19 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. - M.5.18 Interpret patterns of multiplication on a hundreds board and/or multiplication table. - NC.3.OA.9 Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. - NC.3.OA.8 Represent, interpret, and solve one-step problems involving multiplication and division. - NC.3.OA.3 Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. - NC.3.OA.7 Identify apparent relationships between corresponding terms. - NC.5.OA.3.a Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. - NC.3.OA.6 Form ordered pairs consisting of corresponding terms from the two patterns. - NC.5.OA.3.b Graph the ordered pairs on a coordinate plane. - NC.5.OA.3.c Classify two-dimensional figures in a hierarchy based on properties. - M.5.26 The student will compare and order whole numbers between 0 and 999. - 2.1c The student will identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999. - 2.1b Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. - NC.5.NF.1.a Represent real-world mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. - M.5.24 Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. - NC.5.NF.1.b The student will read, write, and identify the place and value of each digit in a three-digit numeral, with and without models. - 2.1a Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category (e.g., all rectangles have four right angles and squares are rectangles, so all squares have four right angles). - M.5.25 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines, the origin, arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). - M.5.23 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - M.5.21 Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). - M.K.10 For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation. - M.K.11 Fluently add and subtract within 5. - M.K.12 Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones (one ten) and one, two, three, four, five, six, seven, eight, or nine ones. - M.K.13 Apply properties of operations as strategies to multiply and divide. - 3.RA.B.6 Describe measurable attributes of objects, such as length or weight and describe several measurable attributes of a single object. - M.K.14 Directly compare two objects with a measurable attribute in common, to see which object has “more of” or “less of” the attribute, and describe the difference. - M.K.15 The student will create and solve single-step story and picture problems using addition and subtraction within 20. - 1.6 Classify objects into given categories, count the numbers of objects in each category, and sort the categories by count. Category counts should be limited to less than or equal to 10. (e.g., Identify coins and sort them into groups of 5s or 10s.) - M.K.16 Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind and next to. - M.K.17 The student will use objects to determine whether a number is even or odd. - 2.2c The student will count backward by tens from 120. - 2.2b The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. - 2.2a Through the use of real-life objects, identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). - M.K.19 Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. - 2.GM.3.1 Building cubes, rectangular prisms, cones, spheres, and cylinders. - NC.1.G.1.b Building and drawing triangles, rectangles, squares, trapezoids, hexagons, circles. - NC.1.G.1.a The student will identify and describe plane figures (circle, triangle, square, and rectangle). - K.10a The student will identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles. - 1.11a The student will identify and describe representations of circles, squares, rectangles, and triangles in different environments, regardless of orientation, and explain reasoning. - 1.11b Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes (e.g., having sides of equal length). Instructional Note: Student focus should include real-world shapes. - M.K.20 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. - M.K.21 The student will read and interpret data represented in pictographs and bar graphs. - 2.15b Compose simple shapes to form larger shapes (e.g., “Can these two triangles, with full sides touching, join to make a rectangle?”). - M.K.22 The student will collect, organize, and represent data in pictographs and bar graphs. - 2.15a Read, write, and compare decimals to thousandths. - NC.5.NBT.3 Explain the patterns in the place value system from one million to the thousandths place. - NC.5.NBT.1 Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. - NC.5.NBT.7 Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two- digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. - NC.5.NBT.6 Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two- digit number using the standard algorithm. - NC.5.NBT.5 Classify quadrilaterals in a hierarchy based on properties. - NC.5.G.3.b Compose and decompose two- and three-dimensional shapes to build an understanding of part-whole relationships and the properties of the original and composite shapes. - 1.GM.A.2 Distinguish between defining attributes versus non-defining attributes; build and draw shapes that possess defining attributes. - 1.GM.A.1 The student will collect, organize, and represent various forms of data using tables, picture graphs, and object graphs. - 1.12a Explain that attributes belonging to a category of quadrilaterals also belong to all subcategories of that category. - NC.5.G.3.a The student will read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to. - 1.12b Partition circles and rectangles into two or four equal shares, and describe the shares and the wholes verbally. - 1.GM.A.4 Add within 100. - 1.NBT.B.5 Calculate 10 more or 10 less than a given number mentally without having to count. - 1.NBT.B.6 The student will represent fractional parts with models and with symbols. - 2.4b The student will name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths. - 2.4a The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. - 4.11 The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. - 4.12 Use tens and ones to make numbers in different ways. - 1.NC.13 The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. - 4.15 The student will recognize and demonstrate the meaning of equality in an equation. - 4.16 Use drawings to solve problems with tens and ones. - 1.NC.12 When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object (one-to-one correspondence). - NC.K.CC.4.a Compare the measurable attributes of two objects. - K.GM.A.2 Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). - 5.N.3.2 Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. - 5.N.3.3 Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. - 5.N.3.1 Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - NC.4.NF.3.a Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. - M.5.15b Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. - NC.4.NF.3.b Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. - M.5.15a Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. - NC.4.NF.3.c Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. - NC.4.NF.3.d The student will demonstrate fluency with addition and subtraction within 20. - 2.5b The student will recognize and use the relationships between addition and subtraction to solve single- step practical problems, with whole numbers to 20. - 2.5a Compose and decompose numbers up to 10 with objects and pictures. - K.N.2.1 Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. - 2.3.2.1 Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. - 2.3.2.2 The student will collect, organize, and represent data. - K.11a The student will compare the size (smaller, larger) and shape of plane figures (circle, triangle, square, and rectangle). - K.10b The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space. - K.10c Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. - 3.GM.2.8 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find are areas of rectangles and represent fraction products as rectangular areas. - M.5.14b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. (e.g., Use a visual fraction model to show (2/3) × 4 = 8/3 and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. - M.5.14a Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. - 3.GM.2.2 Find perimeter of polygon, given whole number lengths of the sides, in real-world and mathematical situations. - 3.GM.2.1 The student will create and solve single-step and two-step practical problems involving addition and subtraction. - 2.6c Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch. - 3.GM.2.4 The student will determine sums and differences, using various methods. - 2.6b Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. - 5.2.2.1 The student will classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles. - 5.13a The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. - 2.7b The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. - 2.7a Draw diagrams and write equations to solve two-step problems involving addition and subtraction of whole numbers. - 3.OA.37 The student will read, write, and identify the place and value of each digit in a nine-digit whole number. - 4.1a Draw diagrams and write equations to solve two-step problems involving multiplication and division of whole numbers. - 3.OA.38 Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer. - 3.OA.39 The student will compare and order whole numbers expressed through millions. - 4.1b The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. - 4.1c Use strategies such as skip counting and properties of operations to multiply. - 3.OA.32 Solve multiplication and division problems that involve different strategies and representations. - 3.OA.33 Use multiplication to write and solve real-world problems involving equal groups. - 3.OA.34 Use division to write and solve real-world problems involving equal groups. - 3.OA.35 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. (e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many1/3-cup servings are in 2 cups of raisins?) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. - M.5.17c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a whole number by a unit fraction and compute such quotients. (e.g., Create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. - M.5.17b Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ?, ??, ???. - K.2.1.1 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. (e.g., Create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.) - M.5.17a Compare two numbers between 1 and 10 presented as written numerals. - M.K.7 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching and counting strategies). - M.K.6 Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. - NC.3.MD.7.a Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1– 20, count out that many objects. - M.K.5 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. - NC.3.OA.7.c Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. - 3.GM.A.1 Understand the relationship between numbers and quantities; connect counting to cardinality. - M.K.4 Know from memory all products with factors up to and including 10. - NC.3.OA.7.a Illustrate and explain using the relationship between multiplication and division. - NC.3.OA.7.b Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), and acting out situations, verbal explanations, expressions, or equations. - M.K.8 Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. - 3.GM.A.3 Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. - 3.GM.A.2 Describe several measureable attributes of objects. - K.GM.A.1 Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning. - NC.3.MD.7.b Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles, and that the area of the large rectangle is the sum of the two smaller rectangles. - NC.3.MD.7.c Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. - 5.RA.C.5 The student will compare and order fractions and mixed numbers, with and without models. - 4.2a The student will represent equivalent fractions. - 4.2b The student will estimate and measure length to the nearest inch. - 2.8a Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). - M.K.3 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). - M.K.2 Count to 100 by ones and by tens. - M.K.1 Divide shapes into 2 and 4 equal shares and use words to describe those shares. - 1.G.10 Convert measurements in a larger unit in terms of a smaller unit. - 4.GM.C.6a Use fraction strips and number lines to add fractions. - 4.NC.49 Use the Associative Property of Multiplication to group 3 factors and multiply. - 3.OA.20 Use benchmarks, area models, and number lines to compare fractions. - 4.NC.46 Use division to find equivalent fractions. - 4.NC.45 Construct arguments about fractions. - 4.NC.48 Use models or rename fractions to compare. - 4.NC.47 Solve problems involving separating parts of the same whole by subtracting fractions. - 4.NC.53 The student will read, write, represent, and identify decimals expressed through thousandths. - 4.3a Use the Distributive Property to solve problems involving multiplication within 100. - 3.OA.14 Use tools such as fraction strips, area models, and number lines to subtract fractions. - 4.NC.52 Use appropriate tools and the Distributive Property to break apart unknown facts with 3 as a factor. - 3.OA.15 The student will round decimals to the nearest whole number. - 4.3b The student will compare and order decimals. - 4.3c Use number lines and benchmark fractions to estimate fraction sums and differences. - 4.NC.55 Use the Distributive Property to break apart unknown facts with 4 as a factor. - 3.OA.16 The student will given a model, write the decimal and fraction equivalents. - 4.3d Count forward or backward on a number line to add or subtract. - 4.NC.54 Use the Distributive Property to break apart unknown facts with 6 or 7 as a factor. - 3.OA.17 Gain fluency in multiplication when multiplying by 0 or 1. - 3.OA.10 Gain fluency in multiplication when multiplying by 10. - 3.OA.11 Solve problems involving joining parts of the same whole by adding fractions. - 4.NC.51 Students will use number relationships and patterns to develop reasoning strategies to support their recall of the basic multiplication facts. - 3.OA.12 Describe the relative positions of objects in space. - K.GM.C.7 Decompose a fraction or mixed number into a sum of fractions in more than one way. - 4.NC.50 Identify shapes and describe objects in the environment using names of shapes, recognizing the name stays the same regardless of orientation or size. - K.GM.C.6 Draw or model simple two-dimensional shapes. - K.GM.C.9 Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes - K.GM.C.8 Use the Distributive Property and known facts to break apart unknown facts with 8 as a factor. - 3.OA.18 Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). - 5.A.2.1 Use strategies such as bar diagrams and arrays with known facts to solve multiplication problems. - 3.OA.19 Solve real-world problems using properties of addition. - 3.NC.1 Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. - 3.N.3.3 Use words to compare objects according to length, size, weight, position, and location. - K.GM.2.1 Construct fractions using length, set, and area models. - 3.N.3.2 Use models and number lines to order and compare fractions that are related to the same whole. - 3.N.3.4 The student, given a practical problem, will represent data in line plots and stem-and-leaf plots. - 5.16a Use mental math to subtract. - 3.NC.5 The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. - 5.16b Use mental math to add. - 3.NC.4 Read and write fractions with words and symbols. - 3.N.3.1 Use place value and a number line to round numbers. - 3.NC.3 Demonstrate that subtraction can be solved as an unknown-addend problem. - 1.RA.B.6 Identify patterns in the addition table and explain them using algebraic thinking. - 3.NC.2 Use partial quotients and place-value understandings to divide with greater dividends. - 4.NC.39 Use properties as strategies to add and subtract. - 1.RA.B.5 Use partial quotients to divide. - 4.NC.38 Solve one-step and multi-step problems using strategies based on the relationship between addition and subtraction. - 3.NC.8 Use a multiplication table to find the missing factor in a division problem. - 3.OA.30 Use rounding or compatible numbers to estimate a difference. - 3.NC.7 Use number sense and reasoning while practicing multiplication and division basic facts. - 3.OA.31 Use rounding or compatible numbers to estimate a sum. - 3.NC.6 Use objects and number lines to represent number sentences. - 2.A.2.1 Use place-value patterns and division facts to estimate quotients for 4-digit dividends. - 4.NC.35 Generate real-world situations to represent number sentences and vice versa. - 2.A.2.2 Use compatible numbers to estimate quotients. - 4.NC.34 Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. - 4.NC.37 Apply commutative and identity properties and number sense to find values for unknowns that make number sentences involving addition and subtraction true or false. - 2.A.2.3 Solve division problems and interpret remainders. - 4.NC.36 The student will estimate and determine sums, differences, and products of whole numbers. - 4.4b Use area models to recognize and generate equivalent fractions. - 4.NC.42 Use properties to understand division involving 0 and 1. - 3.OA.25 The student will estimate and determine quotients of whole numbers, with and without remainders. - 4.4c Use patterns and known facts to find unknown multiplication facts. Use multiplication facts to find related division facts. - 3.OA.26 Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.41 The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. - 4.4d Use multiplication to find equivalent fractions. - 4.NC.44 Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. - 2.2.2.2 Use multiplication and division facts to find unknown values in equations. - 3.OA.27 Use a number line to locate and identify equivalent fractions. - 4.NC.43 Use multiplication facts to divide. - 3.OA.22 Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.40 Use multiplication facts to find related division facts. - 3.OA.23 Use knowledge of even and odd numbers to identify multiplication patterns. - 3.OA.24 Use the multiplication table and the Distributive Property to find patterns in factors and products. - 3.OA.29 The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. - 4.4a Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common. - K.A.1.1 Add to/Take from-Start Unknown - NC.2.OA.1.a.1 Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. - K.3.1.1 Compare-Bigger Unknown - NC.2.OA.1.a.2 Sort objects using characteristics such as shape, size, color and thickness. - K.3.1.2 Compare-Smaller Unknown - NC.2.OA.1.a.3 Use fractions or decimals to solve word problems involving money. - 4.NC.68 Add fractions with denominators of 10 and 100 by using equivalent fractions. - 4.NC.67 Use basic shapes and spatial reasoning to model objects in the real-world. - K.3.1.3 Use the structure of the place-value system for decimals to solve problems. - 4.NC.69 The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. - 4.5c Calculate area by using unit squares to cover a plane figure with no gaps or overlaps. - 3.GM.C.9 Use area and length models to multiply two fractions, with the denominators 2, 3, 4. - NC.5.NF.4.a Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number. - NC.5.NF.4.b The student will add and subtract fractions and mixed numbers having like and unlike denominators. - 4.5b Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. - NC.5.NF.4.c Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements. - 1.N.1.1 Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. - 1.N.1.3 Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. - 1.N.1.2 Find a number that is 10 more or 10 less than a given number up to 100. - 1.N.1.5 Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s. - 1.N.1.4 Use equivalent fractions and properties of operations to add mixed numbers with like denominators. - 4.NC.57 Use knowledge of number relationships to locate the position of a given whole number on an open number line up to 20. - 1.N.1.7 Use models and equivalent fractions to add and subtract mixed numbers. - 4.NC.56 Compare and order whole numbers from 0 to 100. - 1.N.1.6 Use a model to understand a fraction as a multiple of a unit fraction. - 4.NC.59 Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. - 4.NC.58 Use objects to represent and use words to describe the relative size of numbers, such as more than, less than, and equal to. - 1.N.1.8 Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. - 4.RA.B.4 Relate fractions and decimals with denominators of 10 to 100. - 4.NC.64 Use the four operations to solve problems involving time. - 4.NC.63 Compare decimals by reasoning about their size. - 4.NC.66 Calculate and interpret the quotient of a whole number by a unit fraction. - 5.NF.B.8b Locate and describe fractions and decimals on number lines. - 4.NC.65 Calculate and interpret the quotient of a unit fraction by a non-zero whole number. - 5.NF.B.8a Use models to multiply fractions by whole numbers. - 4.NC.60 Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. - 4.NF.C.12 Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. - 4.NC.62 Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. - 4.RA.B.5 Use symbols and equations to multiply a fraction by a whole number. - 4.NC.61 Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. - 4.NF.C.11 Understand that fractions and decimals are equivalent representations of the same quantity. - 4.NF.C.10 The student will add and subtract with decimals. - 4.6a The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. - 4.6b Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. (e.g., Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15c Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15b Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15a Use different strategies to solve word problems with 3 addends. - 1.OA.39 Find the missing numbers in equations to make them true. - 1.OA.38 Determine if addition and subtraction equations are true or false. - 1.OA.37 Count to 100 by ones and tens. - K.NS.A.1 Construct math arguments using fractions. - 3.NC.36 Count forward beginning from a given number between 1 and 20. - K.NS.A.2 Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, = or < and justify the conclusions (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15d Use fraction names to represent whole numbers. - 3.NC.35 Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. - 3.2.2.1 Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. - 3.2.2.2 Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. - 4.NC.11 Use number sense and regrouping to subtract across zeros. - 4.NC.10 Interpret the factors as representing the number of equal groups and the number of objects in each group. - NC.3.OA.1.a Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. - NC.3.OA.1.b Solve word problems involving comparisons. - 1.OA.41 Put together/Take Apart-Addend Unknown - NC.1.OA.1.b Add to/Take from-Change Unknown - NC.1.OA.1.a Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (e.g., Given that a/b represents 3/4 or 6/4, students partition the number line into fourths and represent these fractions accurately on the same number line; students extend the number line to include the number of wholes required for the given fractions.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.14b Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (e.g., Given that b parts is 4 parts, then 1/b represents 1/4. Students partition the number line into fourths and locate 1/4 on the number line.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.14a Compose larger shapes from simple shapes. - NC.K.G.6 Identify squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres as two- dimensional or three-dimensional. - NC.K.G.3 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, attributes and other properties. - NC.K.G.4 Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. - 4.3.2.4 Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. - 4.3.2.3 Compare angles according to size. Classify angles as acute, right and obtuse. - 4.3.2.2 Measure angles in geometric figures and real-world objects with a protractor or angle ruler. - 4.3.2.1 Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. - 4.GM.1.1 Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. - 4.GM.1.2 Use decimal notation for fractions with denominators of 10 or 100. - 4.NF.C.9 Count backward from a given number between 10 and 1. - K.NS.A.3 Read and write numerals and represent a number of objects from 0 to 20. - K.NS.A.4 Describe objects in the environment using names of shapes, and describe the relative positions of objects using positional terms. - NC.K.G.1 The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. - 4.8c The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. - 4.8d Use an open number line to add 3-digit numbers. - 2.NC.47 Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. - 2.1.2.4 Use different strategies to find products when one factor is a multiple of 10. - 3.NC.19 Add 3-digit numbers using mental math strategies. - 2.NC.48 Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. - 2.1.2.1 Use properties of multiplication to find products when one factor is a multiple of 10. - 3.NC.18 Add 3-digit numbers using partial sums. - 2.NC.49 Demonstrate fluency with basic addition facts and related subtraction facts. - 2.1.2.2 Use an open number line to find products when one factor is a multiple of 10. - 3.NC.17 Subtract a 3-digit number from another 3-digit number with one or more zeros by using the standard algorithm. - 3.NC.15 Subtract 3-digit numbers using the standard algorithm. - 3.NC.14 Subtract multi-digit numbers using the expanded algorithm. - 3.NC.13 Make sense of problems and persevere in solving them. - 4.MP.1 Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. - 4.NC.28 Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. - 5.3.2.4 Reason abstractly and quantitatively. - 4.MP.2 Use the Distributive Property and an area model to multiply two 2-digit numbers. - 4.NC.27 Construct viable arguments and critique the reasoning of others. - 4.MP.3 Model with mathematics. - 4.MP.4 Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. - 4.NC.29 Use appropriate tools strategically. - 4.MP.5 Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. - 4.NC.24 Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. - 5.3.2.1 Attend to precision. - 4.MP.6 Use models and properties of operations to multiply 2-digit numbers by multiples of ten. - 4.NC.23 Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. - 5.3.2.3 Look for and make use of structure. - 4.MP.7 Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. - 4.NC.26 Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. - 5.3.2.2 Look for and express regularity in repeated reasoning. - 4.MP.8 Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. - 4.NC.25 Use models and algorithms to solve 2-digit by 2-digit multiplication problems. - 4.NC.31 Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. - 4.NC.30 The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. - K.6 Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. - 4.NC.33 Make sense of problems and persevere in solving them. - 4.NC.32 Make the numbers 14, 15, and 16. - K.NC.2 Make the numbers 17, 18, and 19. - K.NC.3 The student will compare two objects or events, using direct comparisons, according to one or more of the following attributes: length (longer, shorter), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder), volume (more, less), and time (longer, shorter). - K.9 Use models to add 3-digit numbers. - 2.NC.50 Determine and draw the whole (unit) given one part (unit fraction). - 3.NC.23 Use different addition strategies and explain why they work. - 2.NC.51 Use a fraction to represent multiple copies of a unit fraction. - 3.NC.22 Understand how to read and write unit fractions for equal-size parts of a region. - 3.NC.21 Subtract 10 or 100 mentally using place-value strategies. - 2.NC.53 Use an open number line to count back to subtract 3-digit numbers. - 2.NC.54 Use an open number line to add up to subtract 3-digit numbers. - 2.NC.55 Use models to subtract 3-digit numbers. - 2.NC.57 Understand place value and count by hundreds to 1,000. - 2.NC.36 Use place-value blocks and drawings to model and write 3-digit numbers. - 2.NC.37 Compare two or more sets of objects and identify which set is equal to, more than or less than the other. - K.NS.C.10 Tell the value of a digit by where it is placed in a number. - 2.NC.38 Find equivalent fractions that name the same part of the whole. - 3.NC.29 Compare two numerals, between 1 and 10, and determine which is more than or less than the other. - K.NS.C.11 Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. - 1.1.2.1 Compare-Difference Unknown - NC.1.OA.1.c Read and write 3-digit numbers in expanded form, standard form, and word form. - 2.NC.39 Decompose numbers less than or equal to 10 in more than one way. - K.RA.A.3 Compose and decompose numbers up to 12 with an emphasis on making ten. - 1.1.2.2 Measure length to the nearest half inch and show the data on a line plot. - 3.NC.27 Make 10 for any number from 1 to 9. - K.RA.A.4 Measure length to the nearest fourth inch and show the data on a line plot. - 3.NC.26 Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. - 1.1.2.3 Represent addition and subtraction within 10. - K.RA.A.1 Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. - 4.2.2.1 Represent fractions greater than 1 on a number line. - 3.NC.25 Demonstrate fluency for addition and subtraction within 5. - K.RA.A.2 Represent fractions on a number line. - 3.NC.24 Use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. - 4.NC.17 Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. - 4.NC.16 Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths. - NC.3.NF.4 Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. - 4.NC.19 Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. - 4.NC.18 Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. - NC.3.NF.2 Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. - NC.2.MD.8.a Write and solve problems involving addition and subtraction within 100. - 2.NBT.C.11 Use rounding to estimate products and check if answers are reasonable. - 4.NC.13 Model sums and differences of decimals. - 5.NC.10 Multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies - 4.NC.12 Use place value and properties of operations to multiply mentally. - 4.NC.15 Use the Distributive Property to multiply larger numbers. - 4.NC.14 Whole dollar amounts, using the $ symbol appropriately. - NC.2.MD.8.b Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. - 4.NC.20 Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. - 4.NC.22 Use previously-learned concepts and skills to represent and solve problems. - 4.NC.21 Organize, represent, and interpret data with up to four categories. - NC.2.MD.10 Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; - NC.3.NF.1 Use a number line to compare fractions. - 3.NC.34 Make and name a number in different ways to show the same value. - 2.NC.40 Use benchmark numbers to compare fractions. - 3.NC.33 Use place-value patterns to mentally count by 1s and 10s from a given number. - 2.NC.41 Use models such as fraction strips to compare fractions that refer to the same whole and have the same numerator. - 3.NC.32 Use models such as fraction strips to compare fractions that refer to the same whole and have the same denominator. - 3.NC.31 Skip count by 5s, 10s, and 100s using a number line. - 2.NC.42 Solve simple put-together, take-apart, and compare problems using information presented in a picture and a bar graph. - NC.2.MD.10.b Compare numbers using place value. - 2.NC.43 Represent equivalent fractions on a number line. - 3.NC.30 Draw a picture graph and a bar graph with a single-unit scale to represent a data set. - NC.2.MD.10.a Add 10 or 100 mentally using place value. - 2.NC.46 Solve one- and two-step problems using addition or subtraction. - 2.NC.25 Exchange 1 ten for 10 ones. - 2.NC.27 Use place value and models to subtract 2-digit and 1-digit numbers. - 2.NC.28 Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. - M.4.1 Use place value and regrouping to subtract. - 2.NC.29 Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. - M.4.2 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) - M.4.5 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). - M.4.6 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. - M.4.3 Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. - M.4.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. - NC.2.OA.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. - M.4.9 Demonstrate fluency with addition and subtraction, within 20, using mental strategies. - NC.2.OA.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. - M.4.7 Use place value understanding to round multi-digit whole numbers to any place. - M.4.8 Estimate solutions to division problems in order to assess the reasonableness of results. - 5.N.1.1 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). - M.4.15b Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). - M.4.15a Strategies based on place value - NC.2.NBT.7.b Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.N.1.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). - M.4.15c Properties of operations - NC.2.NBT.7.c Relationship between addition and subtraction - NC.2.NBT.7.d Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. - 5.N.1.2 Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. - 5.N.1.3 Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. - NC.3.OA.3.a Demonstrate fluency with addition and subtraction of whole numbers. - 4.NBT.A.5 Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. - 4.2.2.2 Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. - 4.NBT.A.6 Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. - NC.3.OA.3.b Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. - 3.1.2.1 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. - 4.NBT.A.7 The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. - 4.10a Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. - 3.1.2.2 Use place value and models to subtract 2-digit numbers. - 2.NC.30 Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. - 3.1.2.3 Use place value to subtract 2-digit numbers. - 2.NC.31 The student will identify and describe intersecting, parallel, and perpendicular lines. - 4.10b Concrete models or drawings - NC.2.NBT.7.a Add to check subtraction. - 2.NC.32 Subtract 2-digit numbers and decide when to regroup and when not to regroup. - 2.NC.33 Use models and equations to solve word problems. - 2.NC.34 Add three or four 2-digit numbers. - 2.NC.14 Use mental math strategies and models to add more than two numbers. - 2.NC.15 Compare and order whole numbers, with and without objects, from 0 to 20. - K.1.1.5 Use drawings, models, and equations to solve one- and two-step problems. - 2.NC.16 Make models to help solve math problems. - 2.NC.17 Use a hundred chart to subtract tens and ones. - 2.NC.18 Use an open number line to subtract tens. - 2.NC.19 Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. - NC.4.MD.1.b Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. - NC.4.MD.1.a Make and interpret a representation of data using a line graph. - NC.5.MD.2.b Collect data by asking a question that yields data that changes over time. - NC.5.MD.2.a Determine whether a survey question will yield categorical or numerical data, or data that changes over time. - NC.5.MD.2.c Count, with and without objects, forward and backward to at least 20. - K.1.1.3 Compare two fractions using the symbols >, = or <, and justify the solution. - 4.NF.A.3 Find a number that is 1 more or 1 less than a given number. - K.1.1.4 Explain and/or illustrate why two fractions are equivalent. - 4.NF.A.1 Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. - K.1.1.1 Recognize and generate equivalent fractions. - 4.NF.A.2 Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. - K.1.1.2 Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. - 5.1.2.3 Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. - 5.1.2.2 Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - M.4.14a Round numbers to the nearest 0.1, 0.01 and 0.001. - 5.1.2.5 Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. - M.4.14c Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). - M.4.14b Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. - M.4.14d Add three or more numbers using the standard algorithm. - 3.NC.12 Add 3-digit numbers using the standard algorithm. - 3.NC.11 Add two 3-digit numbers by breaking apart problems into simpler problems. - 3.NC.10 Use an open number line to subtract tens and ones. - 2.NC.20 Add up to subtract using an open number line. - 2.NC.21 Break apart 1-digit numbers to make it easier to subtract mentally. - 2.NC.22 Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. - 2.1.2.5 Break apart 2-digit numbers to make it easier to subtract. - 2.NC.23 Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. - 2.1.2.6 Solve problems involving the conversion of one measure of time to another. - 4.GM.3.2 Make numbers that are easier to subtract, and use mental math to find the difference. - 2.NC.24 Use a hundred chart to subtract a multiple of 10 from another multiple of 10. - 1.NC.30 Use attributes to describe different objects. - K.MD.8 Use standard units to measure the area of a shape. - 3.MD.3 Use unit squares to find the area of a figure. - 3.MD.2 Compare objects by length and height. - K.MD.5 Use unit squares to find the area of a shape. - 3.MD.1 Use areas of rectangles to find the area of irregular shapes. - 3.MD.6 Investigate the relationship between two numeric patterns. - 5.RA.A.1 Use areas of rectangles to model the Distributive Property of Multiplication. - 3.MD.5 Write a rule to describe or explain a given numeric pattern. - 5.RA.A.2 Use unit squares and multiplication to find the areas of squares and rectangles. - 3.MD.4 Use frequency tables and picture graphs to compare and interpret data. - 3.MD.9 Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. - 5.1.2.1 Use graphs to compare and interpret data. - 3.MD.8 Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0. - NC.3.NF.2.b Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction. - NC.3.NF.2.a Add 2 two-digit numbers. - 1.NC.26 Add using place value and partial sums. - 2.NC.10 Add numbers using partial sums. - 2.NC.11 Use models to add 2-digit numbers and then explain the work. - 2.NC.12 Add 2-digit numbers and then explain the work. - 2.NC.13 Order three objects by length; compare the lengths of two objects indirectly by using a third object. - NC.1.MD.1 Add 2 multiples of 10. - 1.NC.20 Use mental math to add tens to two-digit numbers. - 1.NC.21 Tell and write time in hours and half-hours using analog and digital clocks. - NC.1.MD.3 Organize, represent, and interpret data with up to three categories. - NC.1.MD.4 Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. - 3.1.2.4 Identify quarters, dimes, and nickels and relate their values to pennies. - NC.1.MD.5 Round multi-digit whole numbers to any place. - 4.NBT.A.1 Solve addition problems by using blocks or drawings. - 1.NC.24 Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. - 3.1.2.5 Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. - 4.NBT.A.2 Interpret comparisons as multiplication or addition equations. - 4.OA.1 Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. - 4.NBT.A.3 Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. - 4.NBT.A.4 Use a number line to solve addition problems. - 1.NC.23 Identify and estimate angles and their measure. - 4.GM.B.4 Draw and measure angles in whole-number degrees using a protractor. - 4.GM.B.5 Compare category counts using appropriate language. - K.DS.A.2 Classify objects into given categories; count the number of objects in each category. - K.DS.A.1 Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. - 4.1.2.2 Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. - 4.1.2.1 Solve two-step problems by finding and solving the hidden question first. - 4.OA.3 Compare two numbers using a greater than, a less than, or an equal to sign. - 1.NC.17 Use multiplication and division to compare two quantities. - 4.OA.2 Count how many objects are in different categories. - K.MD.2 Understand the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: - M.1.10 Make sense of a multi-step problem and keep working until it is solved. - 4.OA.5 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. - M.1.11 Classify objects into categories and tell why they are in each category. - K.MD.1 Solve multi-step problems by finding and solving hidden questions first. - 4.OA.4 Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. - M.1.12 Use place-value blocks to compare 2 two-digit numbers. - 1.NC.16 Use multiplication to find all the factor pairs for a whole number. - 4.OA.7 Use arrays to find the factors of a given whole number. - 4.OA.6 Use factors to determine whether a whole number greater than 1 is prime or composite. - 4.OA.9 Use repeated reasoning to generalize how to solve problems that are similar. - 4.OA.8 List of all Files Validated: imsmanifest.xml I_00053468-a607-3d39-b788-984a7a2bb79e_R/BasicLTI.xml I_001669fc-a133-3f8c-aa49-c8f6e75b1cd1_1_R/BasicLTI.xml I_00233036-c2d2-39ea-a7f2-a0b167de088b_1_R/BasicLTI.xml I_002eeec6-972f-3fc6-aaaa-d46efff7af85_R/BasicLTI.xml I_0043b64f-63bd-322c-bd50-29ef0f9205b6_R/BasicLTI.xml I_00555296-9cbd-3960-8156-1f5b96744cbb_1_R/BasicLTI.xml I_006d1079-5b8f-3fa4-8f00-3e1ad14af05f_1_R/BasicLTI.xml 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I_ff933f0e-450a-34e7-9d11-13d11da3df2a_1_R/BasicLTI.xml I_ffd4af52-8519-3df4-90a4-1a44c9c11b57_1_R/BasicLTI.xml I_ffd4af52-8519-3df4-90a4-1a44c9c11b57_3_R/BasicLTI.xml I_fff183a3-bed5-3488-be09-858725756d2c_R/BasicLTI.xml Title: enVisionmath2.0 Grade 4 2017 Description: enVisionmath2.0 Grade 4 2017 Grade 4 Learning Centers for Students Topic 1: Generalize Place Value Understanding 1-1: Numbers Through One Million Numbers Through One Million: Visual Learning Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Topic 1: Today's Challenge 1-1: Reteach to Build Understanding Worksheet Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-1: Math and Science Activity Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Game: Gobbling Globs - Ten Thousands and Hundred Thousands Numbers Through One Million: Another Look Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-2: Place Value Relationships Place Value Relationships: Visual Learning Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Topic 1: Today's Challenge 1-2: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-2: Math and Science Activity Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Game: Gobbling Globs - Ten Thousands and Hundred Thousands Place Value Relationships: Another Look Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-3: Compare Whole Numbers Compare Whole Numbers: Visual Learning Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Topic 1: Today's Challenge 1-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-3: Problem-Solving Reading Activity Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Compare Whole Numbers: Another Look Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-4: Round Whole Numbers Round Whole Numbers: Visual Learning Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Topic 1: Today's Challenge 1-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-4: Center Games Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Game: Gobbling Globs - Ten Thousands and Hundred Thousands Round Whole Numbers: Another Look Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-5: Problem Solving: Construct Arguments Problem Solving: Construct Arguments: Visual Learning Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Topic 1: Today's Challenge 1-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 1-5: Problem-Solving Reading Activity Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Digital Math Tool Activities Problem Solving: Construct Arguments: Another Look Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Topic 2: Fluently Add and Subtract Multi-Digit Whole Numbers 2-1: Mental Math: Find Sums and Differences Mental Math: Find Sums and Differences: Visual Learning Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Topic 2: Today's Challenge 2-1: Reteach to Build Understanding Worksheet Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-1: Center Games Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Game: AddIt - Adding Three Numbers Mental Math: Find Sums and Differences: Another Look Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-2: Mental Math: Estimate Sums and Differences Mental Math: Estimate Sums and Differences: Visual Learning Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 2: Today's Challenge 2-2: Reteach to Build Understanding Worksheet Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-2: Math and Science Activity Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: AddIt - Adding Three Numbers Mental Math: Estimate Sums and Differences: Another Look Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-3: Add Whole Numbers Add Whole Numbers: Visual Learning Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 2: Today's Challenge 2-3: Reteach to Build Understanding Worksheet Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-3: Problem-Solving Reading Activity Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Add Whole Numbers: Another Look Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Subtract Whole Numbers Subtract Whole Numbers: Visual Learning Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 2: Today's Challenge 2-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Problem-Solving Reading Activity Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Subtract Whole Numbers: Another Look Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-5: Subtract Across Zeros Subtract Across Zeros: Visual Learning Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Topic 2: Today's Challenge 2-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-5: Center Games Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Digital Math Tool Activities Subtract Across Zeros: Another Look Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-6: Problem Solving: Reasoning Problem Solving: Reasoning: Visual Learning Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Topic 2: Today's Challenge 2-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. 2-6: Math and Science Activity Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Digital Math Tool Activities Problem Solving: Reasoning: Another Look Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Topic 3: Use Strategies and Properties to Multiply by 1-Digit Numbers 3-1: Mental Math: Multiply by Multiples of 10, 100, and 1,000 Mental Math: Multiply by Multiples of 10, 100, and 1,000: Visual Learning Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Topic 3: Today's Challenge 3-1: Reteach to Build Understanding Worksheet Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-1: Center Games Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Digital Math Tool Activities Mental Math: Multiply by Multiples of 10, 100, and 1,000: Another Look Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-2: Mental Math: Round to Estimate Products Mental Math: Round to Estimate Products: Visual Learning Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 3: Today's Challenge 3-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-2: Center Games Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers Mental Math: Round to Estimate Products: Another Look Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-3: The Distributive Property The Distributive Property: Visual Learning Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Topic 3: Today's Challenge 3-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-3: Center Games Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers The Distributive Property: Another Look Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-4: Mental Math Strategies for Multiplication Topic 3: Today's Challenge 3-4: Problem-Solving Reading Activity Curriculum Standards: Use place value and properties of operations to multiply mentally. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-5: Arrays and Partial Products Arrays and Partial Products: Visual Learning Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Topic 3: Today's Challenge 3-5: Math and Science Activity Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Game: Power House - Equal Groups to 25 Arrays and Partial Products: Another Look Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-6: Use Partial Products to Multiply by 1-Digit Numbers Topic 3: Today's Challenge Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers 3-7: Multiply 2- and 3-Digit Numbers by 1-Digit Numbers Multiply 2- and 3-Digit Numbers by 1-Digit Numbers: Visual Learning Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 3: Today's Challenge 3-7: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-7: Center Games Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers Multiply 2- and 3-Digit Numbers by 1-Digit Numbers: Another Look Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-8: Multiply 4-Digit by 1-Digit Numbers Topic 3: Today's Challenge 3-8: Center Games Curriculum Standards: Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers Multiply 4-Digit by 1-Digit Numbers: Another Look Curriculum Standards: Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-9: Multiply by 1-Digit Numbers Multiply by 1-Digit Numbers: Visual Learning Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one- digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 3: Today's Challenge 3-9: Reteach to Build Understanding Worksheet Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one- digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-9: Math and Science Activity Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one- digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers 3-10: Problem Solving: Model with Math Topic 3: Today's Challenge 3-10: Center Games Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Model with mathematics. Model with mathematics. Topic 4: Use Strategies and Properties to Multiply by 2-Digit Numbers 4-1: Mental Math: Multiply Multiples of 10 Mental Math: Multiply Multiples of 10: Visual Learning Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 4: Today's Challenge 4-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-1: Center Games Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers Mental Math: Multiply Multiples of 10: Another Look Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-2: Use Models to Multiply 2-Digit Numbers by Multiples of 10 Use Models to Multiply 2-Digit Numbers by Multiples of 10: Visual Learning Curriculum Standards: Use models and properties of operations to multiply 2-digit numbers by multiples of ten. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Topic 4: Today's Challenge 4-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use models and properties of operations to multiply 2-digit numbers by multiples of ten. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-2: Center Games Curriculum Standards: Use models and properties of operations to multiply 2-digit numbers by multiples of ten. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Game: Cosmic Caravan - Arrays and Multiplication Use Models to Multiply 2-Digit Numbers by Multiples of 10: Another Look Curriculum Standards: Use models and properties of operations to multiply 2-digit numbers by multiples of ten. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-3: Estimate: Use Rounding Estimate: Use Rounding: Visual Learning Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 4: Today's Challenge 4-3: Reteach to Build Understanding Worksheet Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-3: Problem-Solving Reading Activity Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Digital Math Tool Activities Estimate: Use Rounding: Another Look Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-4: Estimate: Use Compatible Numbers Estimate: Use Compatible Numbers: Visual Learning Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Topic 4: Today's Challenge 4-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-4: Center Games Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Digital Math Tool Activities Estimate: Use Compatible Numbers: Another Look Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-5: Arrays and Partial Products Topic 4: Today's Challenge 4-5: Math and Science Activity Curriculum Standards: Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Cosmic Caravan - Arrays and Multiplication 4-6: Multiply Using the Distributive Property Multiply Using the Distributive Property: Visual Learning Curriculum Standards: Use the Distributive Property and an area model to multiply two 2- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Topic 4: Today's Challenge 4-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use the Distributive Property and an area model to multiply two 2- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-6: Center Games Curriculum Standards: Use the Distributive Property and an area model to multiply two 2- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Digital Math Tool Activities Multiply Using the Distributive Property: Another Look Curriculum Standards: Use the Distributive Property and an area model to multiply two 2- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-7: Use Partial Products to Multiply by 2-Digit Numbers Topic 4: Today's Challenge Game: Cosmic Caravan - Arrays and Multiplication 4-8: Multiply 2-Digit Numbers by Multiples of 10 Topic 4: Today's Challenge Multiply 2-Digit Numbers by Multiples of 10: Another Look Curriculum Standards: Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3- digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one- digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Multiply 2-Digit by 2-Digit Numbers Multiply 2-Digit by 2-Digit Numbers: Visual Learning Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 4: Today's Challenge 4-9: Reteach to Build Understanding Worksheet Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Problem-Solving Reading Activity Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Multo - 2-Digit Numbers Multiply 2-Digit by 2-Digit Numbers: Another Look Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Continue to Multiply by 2-Digit Numbers Continue to Multiply by 2-Digit Numbers: Visual Learning Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 4: Today's Challenge 4-10: Reteach to Build Understanding Worksheet Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Math and Science Activity Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Multo - 2-Digit Numbers Continue to Multiply by 2-Digit Numbers: Another Look Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-11: Problem Solving: Make Sense & Persevere Problem Solving: Make Sense & Persevere: Visual Learning Curriculum Standards: Make sense of problems and persevere in solving them. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Topic 4: Today's Challenge 4-11: Reteach to Build Understanding Worksheet Curriculum Standards: Make sense of problems and persevere in solving them. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 4-11: Center Games Curriculum Standards: Make sense of problems and persevere in solving them. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Game: Save the Word: Grade 4 Topics 1–4 Problem Solving: Make Sense & Persevere: Another Look Curriculum Standards: Make sense of problems and persevere in solving them. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Topic 5: Use Strategies and Properties to Divide by 1-Digit Numbers 5-1: Mental Math: Find Quotients Mental Math: Find Quotients: Visual Learning Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Topic 5: Today's Challenge 5-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-1: Center Games Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Find Quotients: Another Look Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Mental Math: Estimate Quotients Mental Math: Estimate Quotients: Visual Learning Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Topic 5: Today's Challenge 5-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Center Games Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Estimate Quotients: Another Look Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Mental Math: Estimate Quotients for Greater Dividends Mental Math: Estimate Quotients for Greater Dividends: Visual Learning Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Topic 5: Today's Challenge 5-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Math and Science Activity Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Estimate Quotients for Greater Dividends: Another Look Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Interpret Remainders Interpret Remainders: Visual Learning Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Topic 5: Today's Challenge 5-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Center Games Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Digital Math Tool Activities Interpret Remainders: Another Look Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-5: Division as Sharing Division as Sharing: Visual Learning Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 5: Today's Challenge 5-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Center Games Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Digital Math Tool Activities Division as Sharing: Another Look Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Use Partial Quotients to Divide Use Partial Quotients to Divide: Visual Learning Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 5: Today's Challenge 5-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Problem-Solving Reading Activity Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Use Partial Quotients to Divide: Another Look Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Use Partial Quotients to Divide: Greater Dividends Use Partial Quotients to Divide: Greater Dividends: Visual Learning Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 5: Today's Challenge 5-7: Reteach to Build Understanding Worksheet Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Math and Science Activity Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Digital Math Tool Activities Use Partial Quotients to Divide: Greater Dividends: Another Look Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-8: Divide with 1-Digit Numbers Divide with 1-Digit Numbers: Visual Learning Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Topic 5: Today's Challenge 5-8: Problem-Solving Reading Activity Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Divide with 1-Digit Numbers: Another Look Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-9: Continue to Divide with 1-Digit Numbers Topic 5: Today's Challenge Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Continue to Divide with 1-Digit Numbers: Another Look Curriculum Standards: Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-10: Problem Solving: Model With Math Topic 5: Today's Challenge 5-10: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Model with mathematics. Model with mathematics. Problem Solving: Model With Math: Another Look Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Model with mathematics. Model with mathematics. Topic 6: Use Operations with Whole Numbers to Solve Problems 6-1: Solve Comparison Situations Solve Comparison Situations: Visual Learning Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Topic 6: Today's Challenge 6-1: Reteach to Build Understanding Worksheet Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-1: Problem-Solving Reading Activity Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Digital Math Tool Activities Solve Comparison Situations: Another Look Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-2: Continue to Solve Comparison Situations Topic 6: Today's Challenge Digital Math Tool Activities 6-3: Solve Multi-Step Problems Solve Multi-Step Problems: Visual Learning Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Topic 6: Today's Challenge 6-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-3: Math and Science Activity Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Solve Multi-Step Problems: Another Look Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Solve More Multi-Step Problems Solve More Multi-Step Problems: Visual Learning Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Topic 6: Today's Challenge 6-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Math and Science Activity Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Solve More Multi-Step Problems: Another Look Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-5: Problem Solving: Make Sense & Persevere Topic 6: Today's Challenge Game: Save the Word: Grade 4 Topics 1–4 Topic 7: Factors and Multiples 7-1: Understand Factors Understand Factors: Visual Learning Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Topic 7: Today's Challenge 7-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-1: Math and Science Activity Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Digital Math Tool Activities Understand Factors: Another Look Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Factors Factors: Visual Learning Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Topic 7: Today's Challenge 7-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Problem-Solving Reading Activity Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Digital Math Tool Activities Factors: Another Look Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-3: Problem Solving: Repeated Reasoning Problem Solving: Repeated Reasoning: Visual Learning Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Topic 7: Today's Challenge 7-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-3: Math and Science Activity Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Digital Math Tool Activities Problem Solving: Repeated Reasoning: Another Look Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-4: Prime and Composite Numbers Prime and Composite Numbers: Visual Learning Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Topic 7: Today's Challenge 7-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-4: Center Games Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Digital Math Tool Activities Prime and Composite Numbers: Another Look Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Multiples Multiples: Visual Learning Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Topic 7: Today's Challenge 7-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Problem-Solving Reading Activity Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Game: Save the Word: Grade 4 Topics 1–4 Multiples: Another Look Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Topic 8: Extend Understanding of Fraction Equivalence and Ordering 8-1: Equivalent Fractions: Area Models Equivalent Fractions: Area Models: Visual Learning Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Topic 8: Today's Challenge 8-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-1: Center Games Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Digital Math Tool Activities Equivalent Fractions: Area Models: Another Look Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Equivalent Fractions: Number Lines Equivalent Fractions: Number Lines: Visual Learning Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Topic 8: Today's Challenge 8-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Center Games Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Digital Math Tool Activities Equivalent Fractions: Number Lines: Another Look Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Generate Equivalent Fractions: Multiplication Generate Equivalent Fractions: Multiplication: Visual Learning Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Topic 8: Today's Challenge 8-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Center Games Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Digital Math Tool Activities Generate Equivalent Fractions: Multiplication: Another Look Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-4: Generate Equivalent Fractions: Division Generate Equivalent Fractions: Division: Visual Learning Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Topic 8: Today's Challenge 8-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-4: Problem-Solving Reading Activity Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Digital Math Tool Activities Generate Equivalent Fractions: Division: Another Look Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-5: Use Benchmarks to Compare Fractions Use Benchmarks to Compare Fractions: Visual Learning Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Topic 8: Today's Challenge 8-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-5: Math and Science Activity Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Use Benchmarks to Compare Fractions: Another Look Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Compare Fractions Compare Fractions: Visual Learning Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Topic 8: Today's Challenge 8-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Math and Science Activity Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Compare Fractions: Another Look Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-7: Problem Solving: Construct Arguments Problem Solving: Construct Arguments: Visual Learning Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Topic 8: Today's Challenge 8-7: Reteach to Build Understanding Worksheet Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 8-7: Problem-Solving Reading Activity Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Game: Save the Word: Grade 4 Topics 1–8 Problem Solving: Construct Arguments: Another Look Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Topic 9: Understand Addition and Subtraction of Fractions 9-1: Model Addition of Fractions Model Addition of Fractions: Visual Learning Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-1: Center Games Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Fancy Flea - Fractions Model Addition of Fractions: Another Look Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Decompose Fractions Decompose Fractions: Visual Learning Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-2: Reteach to Build Understanding Worksheet Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Math and Science Activity Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Decompose Fractions: Another Look Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Add Fractions with Like Denominators Add Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Center Games Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Fancy Flea - Fractions Add Fractions with Like Denominators: Another Look Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Model Subtraction of Fractions Model Subtraction of Fractions: Visual Learning Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Center Games Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Model Subtraction of Fractions: Another Look Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Subtract Fractions with Like Denominators Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-5: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Center Games Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Gem Quest - Fractions Subtract Fractions with Like Denominators: Another Look Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Add and Subtract Fractions with Like Denominators Add and Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-6: Reteach to Build Understanding Worksheet Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Problem-Solving Reading Activity Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Flying Cow Incident - 2-Digit Numbers Add and Subtract Fractions with Like Denominators: Another Look Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-7: Estimate Fraction Sums and Differences Estimate Fraction Sums and Differences: Visual Learning Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Topic 9: Today's Challenge 9-7: Reteach to Build Understanding Worksheet Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-7: Math and Science Activity Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Game: Fancy Flea - Fractions Estimate Fraction Sums and Differences: Another Look Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-8: Model Addition and Subtraction of Mixed Numbers Model Addition and Subtraction of Mixed Numbers: Visual Learning Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-8: Reteach to Build Understanding Worksheet Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-8: Center Games Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Model Addition and Subtraction of Mixed Numbers: Another Look Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Add Mixed Numbers Add Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-9: Reteach to Build Understanding Worksheet Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Center Games Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Add Mixed Numbers: Another Look Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Subtract Mixed Numbers Subtract Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9: Today's Challenge 9-10: Reteach to Build Understanding Worksheet Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Center Games Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Subtract Mixed Numbers: Another Look Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-11: Problem Solving: Model with Math Problem Solving: Model with Math: Visual Learning Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Topic 9: Today's Challenge 9-11: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. 9-11: Problem-Solving Reading Activity Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Game: Save the Word: Grade 4 Topics 1–8 Problem Solving: Model with Math: Another Look Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Topic 10: Extend Multiplication Concepts to Fractions 10-1: Fractions as Multiples of Unit Fractions: Use Models Fractions as Multiples of Unit Fractions: Use Models: Visual Learning Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Topic 10: Today's Challenge 10-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-1: Problem-Solving Reading Activity Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Fractions as Multiples of Unit Fractions: Use Models: Another Look Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Multiply a Fraction by a Whole Number: Use Models Multiply a Fraction by a Whole Number: Use Models: Visual Learning Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Topic 10: Today's Challenge 10-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Math and Science Activity Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Multiply a Fraction by a Whole Number: Use Models: Another Look Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Multiply a Fraction by a Whole Number: Use Symbols Multiply a Fraction by a Whole Number: Use Symbols: Visual Learning Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Topic 10: Today's Challenge 10-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Center Games Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Multiply a Fraction by a Whole Number: Use Symbols: Another Look Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Multiply a Whole Number and a Mixed Number Multiply a Whole Number and a Mixed Number: Visual Learning Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Topic 10: Today's Challenge 10-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Problem-Solving Reading Activity Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Multiply a Whole Number and a Mixed Number: Another Look Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-5: Solve Time Problems Solve Time Problems: Visual Learning Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 10: Today's Challenge 10-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Center Games Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Solve Time Problems: Another Look Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-6: Problem Solving: Model With Math Problem Solving: Model With Math: Visual Learning Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric). Model with mathematics. Model with mathematics. Topic 10: Today's Challenge 10-6: Math and Science Activity Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric). Model with mathematics. Model with mathematics. Game: Save the Word: Grade 4 Topics 1–8 Topic 11: Represent and Interpret Data on Line Plots 11-1: Read Line Plots Read Line Plots: Visual Learning Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Topic 11: Today's Challenge 11-1: Reteach to Build Understanding Worksheet Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-1: Math and Science Activity Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Game: Factory Frenzy - Fractions Read Line Plots: Another Look Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Make Line Plots Make Line Plots: Visual Learning Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Topic 11: Today's Challenge 11-2: Reteach to Build Understanding Worksheet Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Problem-Solving Reading Activity Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Digital Math Tool Activities Make Line Plots: Another Look Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Use Line Plots to Solve Problems Use Line Plots to Solve Problems: Visual Learning Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Topic 11: Today's Challenge 11-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Math and Science Activity Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Digital Math Tool Activities Use Line Plots to Solve Problems: Another Look Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-4: Problem Solving: Critique Reasoning Topic 11: Today's Challenge 11-4: Reteach to Build Understanding Worksheet Curriculum Standards: Critique the reasoning of others using an understanding of line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 11-4: Problem-Solving Reading Activity Curriculum Standards: Critique the reasoning of others using an understanding of line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Game: Save the Word: Grade 4 Topics 1–8 Topic 12: Undertand and Compare Decimals 12-1: Fractions and Decimals Fractions and Decimals: Visual Learning Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Topic 12: Today's Challenge 12-1: Reteach to Build Understanding Worksheet Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-1: Center Games Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Digital Math Tool Activities Fractions and Decimals: Another Look Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Fractions and Decimals on the Number Line Fractions and Decimals on the Number Line: Visual Learning Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Topic 12: Today's Challenge 12-2: Reteach to Build Understanding Worksheet Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Problem-Solving Reading Activity Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Digital Math Tool Activities Fractions and Decimals on the Number Line: Another Look Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-3: Compare Decimals Compare Decimals: Visual Learning Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Topic 12: Today's Challenge 12-3: Reteach to Build Understanding Worksheet Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-3: Center Games Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Compare Decimals: Another Look Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-4: Add Fractions with Denominators of 10 and 100 Add Fractions with Denominators of 10 and 100: Visual Learning Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 12: Today's Challenge 12-4: Reteach to Build Understanding Worksheet Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-4: Problem-Solving Reading Activity Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Add Fractions with Denominators of 10 and 100: Another Look Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-5: Solve Word Problems Involving Money Solve Word Problems Involving Money: Visual Learning Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 12: Today's Challenge 12-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-5: Math and Science Activity Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Solve Word Problems Involving Money: Another Look Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-6: Problem Solving: Look For & Use Structure Problem Solving: Look For & Use Structure: Visual Learning Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Topic 12: Today's Challenge 12-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. 12-6: Math and Science Activity Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Game: Save the Word: Grade 4 Topics 1–12 Problem Solving: Look For & Use Structure: Another Look Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Topic 13: Measurement: Find Equivalence in Units of Measure 13-1: Equivalence with Customary Units of Length Equivalence with Customary Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 13: Today's Challenge 13-1: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1 Center Games Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Customary Units of Length: Another Look Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Equivalence with Customary Units of Capacity Equivalence with Customary Units of Capacity: Visual Learning Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 13: Today's Challenge 13-2: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2 Math and Science Activity Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Customary Units of Capacity: Another Look Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Equivalence with Customary Units of Weight Equivalence with Customary Units of Weight: Visual Learning Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 13: Today's Challenge 13-3: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3 Problem-Solving Reading Activity Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Customary Units of Weight: Another Look Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Equivalence with Metric Units of Length Equivalence with Metric Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 13: Today's Challenge 13-4: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4 Center Games Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Game: Galaxy Hunt - Make a Million Equivalence with Metric Units of Length: Another Look Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Equivalence with Metric Units of Capacity and Mass Equivalence with Metric Units of Capacity and Mass: Visual Learning Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 13: Today's Challenge 13-5: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5 Math and Science Activity Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Metric Units of Capacity and Mass: Another Look Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-6: Solve Perimeter and Area Problems Solve Perimeter and Area Problems: Visual Learning Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Topic 13: Today's Challenge 13-6: Reteach to Build Understanding Worksheet Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-6 Center Games Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Digital Math Tool Activities Solve Perimeter and Area Problems: Another Look Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-7: Problem Solving: Precision Problem Solving: Precision: Visual Learning Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Topic 13: Today's Challenge 13-7: Reteach to Build Understanding Worksheet Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. 13-7 Problem-Solving Reading Activity Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Game: Save the Word: Grade 4 Topics 1–12 Problem Solving: Precision: Another Look Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Topic 14: Algebra: Generate and Analyze Patterns 14-1: Number Sequences Number Sequences: Visual Learning Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Topic 14: Today's Challenge 14-1: Reteach to Build Understanding Worksheet Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-1 Problem-Solving Reading Activity Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Number Sequences: Another Look Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Patterns: Number Rules Patterns: Number Rules: Visual Learning Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Topic 14: Today's Challenge 14-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2 Problem-Solving Reading Activity Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Digital Math Tool Activities Patterns: Number Rules: Another Look Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Patterns: Repeating Shapes Patterns: Repeating Shapes: Visual Learning Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Topic 14: Today's Challenge 14-3: Reteach to Build Understanding Worksheet Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3 Math and Science Activity Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Digital Math Tool Activities Patterns: Repeating Shapes: Another Look Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-4: Problem Solving: Look For & Use Structure Problem Solving: Look For & Use Structure: Visual Learning Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Topic 14: Today's Challenge 14-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. 14-4 Math and Science Activity Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Digital Math Tool Activities Problem Solving: Look For & Use Structure: Another Look Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Topic 15: Understand Concepts of Angle and Angle Measurement 15-1: Lines, Rays, and Angles Lines, Rays, and Angles: Visual Learning Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Topic 15: Today's Challenge 15-1: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Center Games Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Digital Math Tool Activities Lines, Rays, and Angles: Another Look Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-2: Understand Angles and Unit Angles Understand Angles and Unit Angles: Visual Learning Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Topic 15: Today's Challenge 15-2: Reteach to Build Understanding Worksheet Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-2: Center Games Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Digital Math Tool Activities Understand Angles and Unit Angles: Another Look Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-3: Measure with Unit Angles Measure with Unit Angles: Visual Learning Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Topic 15: Today's Challenge 15-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Problem-Solving Reading Activity Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Digital Math Tool Activities Measure with Unit Angles: Another Look Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-4: Measure and Draw Angles Measure and Draw Angles: Visual Learning Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Topic 15: Today's Challenge 15-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-4: Math and Science Activity Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Game: Save the Word: Grade 4 Topics 1–12 Measure and Draw Angles: Another Look Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-5: Add and Subtract Angle Measures Add and Subtract Angle Measures: Visual Learning Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Topic 15: Today's Challenge 15-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-5: Math and Science Activity Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Digital Math Tool Activities Add and Subtract Angle Measures: Another Look Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-6: Problem Solving: Use Appropriate Tools Problem Solving: Use Appropriate Tools: Visual Learning Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Topic 15: Today's Challenge 15-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. 15-6: Problem-Solving Reading Activity Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Digital Math Tool Activities Problem Solving: Use Appropriate Tools: Another Look Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Topic 16: Lines, Angles, and Shapes 16-1: Lines Lines: Visual Learning Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Topic 16: Today's Challenge 16-1: Reteach to Build Understanding Worksheet Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-1: Center Games Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Digital Math Tool Activities Lines: Another Look Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-2: Classify Triangles Classify Triangles: Visual Learning Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Topic 16: Today's Challenge 16-2: Reteach to Build Understanding Worksheet Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-2: Center Games Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Digital Math Tool Activities Classify Triangles: Another Look Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-3: Classify Quadrilaterals Classify Quadrilaterals: Visual Learning Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Topic 16: Today's Challenge 16-3: Reteach to Build Understanding Worksheet Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-3: Problem-Solving Reading Activity Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Digital Math Tool Activities Classify Quadrilaterals: Another Look Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-4: Line Symmetry Line Symmetry: Visual Learning Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Topic 16: Today's Challenge 16-4: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-4: Math and Science Activity Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Digital Math Tool Activities Line Symmetry: Another Look Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Draw Shapes with Line Symmetry Draw Shapes with Line Symmetry: Visual Learning Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Topic 16: Today's Challenge 16-5: Reteach to Build Understanding Worksheet Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Math and Science Activity Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Game: Save the Word: Grade 4 Topics 1–16 Draw Shapes with Line Symmetry: Another Look Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-6: Problem Solving: Critique Reasoning Problem Solving: Critique Reasoning: Visual Learning Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Topic 16: Today's Challenge 16-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 16-6: Problem-Solving Reading Activity Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Game: Save the Word: Grade 4 Topics 1–16 Problem Solving: Critique Reasoning: Another Look Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Online Placement Test Curriculum Standards: Use number lines to join equal groups. Use arrays as one way to think about and understand multiplication. Understand and use the Commutative Property of Multiplication. Gain fluency in multiplication when multiplying by 0 or 1. Use the Distributive Property to break apart unknown facts with 4 as a factor. Use multiplication facts to divide. Use multiplication facts to find related division facts. Use a multiplication table to find the missing factor in a division problem. Solve multiplication and division problems that involve different strategies and representations. Use unit squares and multiplication to find the areas of squares and rectangles. Use areas of rectangles to find the area of irregular shapes. Use graphs to compare and interpret data. Use graphs to solve problems. Use place value and a number line to round numbers. Use mental math to subtract. Use rounding or compatible numbers to estimate a sum. Add 3-digit numbers using the standard algorithm. Use different strategies to find products when one factor is a multiple of 10. Draw diagrams and write equations to solve two-step problems involving addition and subtraction of whole numbers. Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer. Use a fraction to represent multiple copies of a unit fraction. Represent fractions on a number line. Solve word problems involving addition and subtraction to measure quantities of time. Use pictures to help solve problems about mass and volume. Identify quadrilaterals and use attributes to describe them. Classify shapes according to their attributes. Find the perimeter of different polygons with common shapes. Use the given sides of a polygon and the known perimeter to find the unknown side length. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Relate area to the operations of multiplication and addition. Recognize area as additive and find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will read and interpret data represented in pictographs and bar graphs. Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Use place value understanding to round whole numbers to the nearest 10 or 100. The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (e.g., Given that b parts is 4 parts, then 1/b represents 1/4. Students partition the number line into fourths and locate 1/4 on the number line.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (e.g., Given that a/b represents 3/4 or 6/4, students partition the number line into fourths and represent these fractions accurately on the same number line; students extend the number line to include the number of wholes required for the given fractions.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). The student will solve practical problems related to elapsed time in one-hour increments within a 12-hour period. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. Instructional Note: Exclude compound units such as cm3 and finding the geometric volume of a container. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. The student will estimate and measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Find the perimeter of a polygon by adding the lengths of the sides. Measure distances around objects. Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. Know relationships among units of time. Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Demonstrate fluency of multiplication facts with factors up to 10. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Read and write fractions with words and symbols. Construct fractions using length, set, and area models. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division to represent and solve real-world problems. Find perimeter of polygon, given whole number lengths of the sides, in real-world and mathematical situations. Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Illustrate and explain using the relationship between multiplication and division. Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares. Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole- number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two- step “how many more” and “how many less” problems using information from these graphs. Solve two- step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. Use estimation strategies to assess reasonableness of answers. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; Explain that a unit fraction is one of those parts. Represent and identify unit fractions using area and length models. Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction. Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. Solve problems involving customary measurement. Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds. Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units. Reason with two-dimensional shapes and their attributes. Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids. Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value. Multiply whole-number side lengths to solve problems involving the area of rectangles. Decompose a rectangle into smaller rectangles to find the area of the original rectangle. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. Write and solve two-step problems involving variables using any of the four operations. Round whole numbers to the nearest 10 or 100. Demonstrate fluency with addition and subtraction within 1000. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply whole numbers by multiples of 10 in the range 10-90. Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole. Describe the numerator as representing the number of pieces being considered. Describe the denominator as the number of pieces that make the whole. Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. Represent fractions on a number line. Understand the whole is the interval from 0 to 1. Understand the whole is partitioned into equal parts. Understand a fraction represents the endpoint of the length a given number of partitions from 0. Tell and write time to the nearest minute. Estimate time intervals in minutes. Solve problems involving addition and subtraction of minutes. Measure or estimate length, liquid volume and weight of objects. Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. Solve problems involving perimeters of polygons. Math Practices Animations Math Practice 1 Animation Math Practice 2 Animation Math Practice 3 Animation Math Practice 4 Animation Math Practice 5 Animation Math Practice 6 Animation Math Practice 7 Animation Math Practice 8 Animation Topic 1: Generalize Place Value Understanding Topic 1: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 1 Math and Science Project Review What You Know Vocabulary Cards 1-1: Numbers Through One Million Student's Edition eText: Grade 4 Lesson 1-1 Interactive Student Edition: Grade 4 Lesson 1-1 Student's Edition ACTIVe-book: Grade 4 Lesson 1-1 Math Anytime Numbers Through One Million: Review Topic 1: Today's Challenge Develop: Problem-Based Learning Numbers Through One Million: Solve & Share Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Develop: Visual Learning Numbers Through One Million: Visual Learning Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Numbers Through One Million: Convince Me! Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Numbers Through One Million: Practice Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Assess & Differentiate 1-1: Homework & Practice Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-1: Homework & Practice Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Numbers Through One Million: Quick Check Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-1: Reteach to Build Understanding Worksheet Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-1: Enrichment Worksheet 1-1: Math and Science Activity Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Game: Gobbling Globs - Ten Thousands and Hundred Thousands Numbers Through One Million: Another Look Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-1: Practice Buddy: Homework & Practice Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-2: Place Value Relationships Student's Edition eText: Grade 4 Lesson 1-2 Interactive Student Edition: Grade 4 Lesson 1-2 Student's Edition ACTIVe-book: Grade 4 Lesson 1-2 Math Anytime Place Value Relationships: Review Topic 1: Today's Challenge Develop: Problem-Based Learning Place Value Relationships: Solve & Share Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Develop: Visual Learning Place Value Relationships: Visual Learning Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Place Value Relationships: Convince Me! Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Place Value Relationships: Practice Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Assess & Differentiate 1-2: Homework & Practice Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-2: Homework & Practice Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Place Value Relationships: Quick Check Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-2: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-2: Enrichment Worksheet 1-2: Math and Science Activity Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Game: Gobbling Globs - Ten Thousands and Hundred Thousands Place Value Relationships: Another Look Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-2: Practice Buddy: Homework & Practice Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. 1-3: Compare Whole Numbers Student's Edition eText: Grade 4 Lesson 1-3 Interactive Student Edition: Grade 4 Lesson 1-3 Student's Edition ACTIVe-book: Grade 4 Lesson 1-3 Math Anytime Compare Whole Numbers: Review Topic 1: Today's Challenge Develop: Problem-Based Learning Compare Whole Numbers: Solve & Share Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Develop: Visual Learning Compare Whole Numbers: Visual Learning Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Compare Whole Numbers: Convince Me! Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Compare Whole Numbers: Practice Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Assess & Differentiate 1-3: Homework & Practice Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-3: Homework & Practice Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Compare Whole Numbers: Quick Check Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-3: Enrichment Worksheet 1-3: Problem-Solving Reading Activity Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Compare Whole Numbers: Another Look Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-3: Practice Buddy: Homework & Practice Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. 1-4: Round Whole Numbers Student's Edition eText: Grade 4 Lesson 1-4 Interactive Student Edition: Grade 4 Lesson 1-4 Student's Edition ACTIVe-book: Grade 4 Lesson 1-4 Math Anytime Round Whole Numbers: Review Topic 1: Today's Challenge Develop: Problem-Based Learning Round Whole Numbers: Solve & Share Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Develop: Visual Learning Round Whole Numbers: Visual Learning Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Round Whole Numbers: Convince Me! Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Round Whole Numbers: Practice Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Assess & Differentiate 1-4: Homework & Practice Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-4: Homework & Practice Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Round Whole Numbers: Quick Check Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-4: Enrichment Worksheet 1-4: Center Games Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Game: Gobbling Globs - Ten Thousands and Hundred Thousands Round Whole Numbers: Another Look Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-4: Practice Buddy: Homework & Practice Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. 1-5: Problem Solving: Construct Arguments Student's Edition eText: Grade 4 Lesson 1-5 Interactive Student Edition: Grade 4 Lesson 1-5 Student's Edition ACTIVe-book: Grade 4 Lesson 1-5 Math Anytime Problem Solving: Construct Arguments: Review Topic 1: Today's Challenge Develop: Problem-Based Learning Problem Solving: Construct Arguments: Solve & Share Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Develop: Visual Learning Problem Solving: Construct Arguments: Visual Learning Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Construct Arguments: Convince Me! Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Construct Arguments: Practice Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 1-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Assess & Differentiate 1-5: Homework & Practice Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 1-5: Homework & Practice Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Construct Arguments: Quick Check Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 1-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 1-5: Enrichment Worksheet 1-5: Problem-Solving Reading Activity Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Digital Math Tool Activities Problem Solving: Construct Arguments: Another Look Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 1-5: Practice Buddy: Homework & Practice Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. End Topic Interactive Student Edition: End Topic 1 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 1 Assessment Interactive Student Edition: Topic 1 Performance Assessment Numbers Through One Million: Visual Learning Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. 1-2: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Place Value Relationships: Visual Learning Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Compare Whole Numbers: Visual Learning Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi- digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi- digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Round Whole Numbers: Visual Learning Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Problem Solving: Construct Arguments: Visual Learning Curriculum Standards: Use previously learned concepts and skills to construct arguments about place value. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will compare and order whole numbers expressed through millions. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Game: Galaxy Hunt - Make a Million Topic 1 Online Assessment Curriculum Standards: Use place value to compare multi-digit numbers. Use previously learned concepts and skills to construct arguments about place value. Use place value to round multi-digit numbers. Recognize the relationship between adjacent digits in a multi-digit number. Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Use place value understanding to round multi-digit whole numbers to any place. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Use an understanding of place value to multiply a number by 10, 100 and 1000. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Topic 2: Fluently Add and Subtract Multi-Digit Whole Numbers Topic 2: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 2 Math and Science Project Review What You Know Vocabulary Cards 2-1: Mental Math: Find Sums and Differences Student's Edition eText: Grade 4 Lesson 2-1 Interactive Student Edition: Grade 4 Lesson 2-1 Student's Edition ACTIVe-book: Grade 4 Lesson 2-1 Math Anytime Mental Math: Find Sums and Differences: Review Topic 2: Today's Challenge Develop: Problem-Based Learning Mental Math: Find Sums and Differences: Solve & Share Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Develop: Visual Learning Mental Math: Find Sums and Differences: Visual Learning Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Mental Math: Find Sums and Differences: Convince Me! Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Mental Math: Find Sums and Differences: Practice Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Assess & Differentiate 2-1: Homework & Practice Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-1: Homework & Practice Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Mental Math: Find Sums and Differences: Quick Check Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-1: Reteach to Build Understanding Worksheet Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-1: Enrichment Worksheet 2-1: Center Games Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Game: AddIt - Adding Three Numbers Mental Math: Find Sums and Differences: Another Look Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-1: Practice Buddy: Homework & Practice Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-2: Mental Math: Estimate Sums and Differences Student's Edition eText: Grade 4 Lesson 2-2 Interactive Student Edition: Grade 4 Lesson 2-2 Student's Edition ACTIVe-book: Grade 4 Lesson 2-2 Math Anytime Mental Math: Estimate Sums and Differences: Review Topic 2: Today's Challenge Develop: Problem-Based Learning Mental Math: Estimate Sums and Differences: Solve & Share Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Mental Math: Estimate Sums and Differences: Visual Learning Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Estimate Sums and Differences: Convince Me! Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Estimate Sums and Differences: Practice Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 2-2: Homework & Practice Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-2: Homework & Practice Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Estimate Sums and Differences: Quick Check Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-2: Reteach to Build Understanding Worksheet Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-2: Enrichment Worksheet 2-2: Math and Science Activity Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: AddIt - Adding Three Numbers Mental Math: Estimate Sums and Differences: Another Look Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-2: Practice Buddy: Homework & Practice Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-3: Add Whole Numbers Interactive Student Edition: Grade 4 Lesson 2-3 2-4: Subtract Whole Numbers Student's Edition eText: Grade 4 Lesson 2-4 Interactive Student Edition: Grade 4 Lesson 2-4 Student's Edition ACTIVe-book: Grade 4 Lesson 2-4 Math Anytime Subtract Whole Numbers: Review Topic 2: Today's Challenge Develop: Problem-Based Learning Subtract Whole Numbers: Solve & Share Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Subtract Whole Numbers: Visual Learning Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Subtract Whole Numbers: Convince Me! Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Subtract Whole Numbers: Practice Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 2-4: Homework & Practice Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Homework & Practice Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Subtract Whole Numbers: Quick Check Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Enrichment Worksheet 2-4: Problem-Solving Reading Activity Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Subtract Whole Numbers: Another Look Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Practice Buddy: Homework & Practice Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-5: Subtract Across Zeros Student's Edition eText: Grade 4 Lesson 2-5 Interactive Student Edition: Grade 4 Lesson 2-5 Student's Edition ACTIVe-book: Grade 4 Lesson 2-5 Math Anytime Subtract Across Zeros: Review Topic 2: Today's Challenge Develop: Problem-Based Learning Subtract Across Zeros: Solve & Share Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Develop: Visual Learning Subtract Across Zeros: Visual Learning Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Subtract Across Zeros: Convince Me! Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Subtract Across Zeros: Practice Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Assess & Differentiate 2-5: Homework & Practice Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-5: Homework & Practice Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Subtract Across Zeros: Quick Check Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-5: Enrichment Worksheet 2-5: Center Games Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Digital Math Tool Activities Subtract Across Zeros: Another Look Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-5: Practice Buddy: Homework & Practice Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. 2-6: Problem Solving: Reasoning Student's Edition eText: Grade 4 Lesson 2-6 Interactive Student Edition: Grade 4 Lesson 2-6 Student's Edition ACTIVe-book: Grade 4 Lesson 2-6 Math Anytime Problem Solving: Reasoning: Review Topic 2: Today's Challenge Develop: Problem-Based Learning Problem Solving: Reasoning: Solve & Share Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Develop: Visual Learning Problem Solving: Reasoning: Visual Learning Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Problem Solving: Reasoning: Convince Me! Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Problem Solving: Reasoning: Practice Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. 2-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Assess & Differentiate 2-6: Homework & Practice Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Problem Solving: Reasoning: Quick Check Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. 2-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. 2-6: Enrichment Worksheet 2-6: Math and Science Activity Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Digital Math Tool Activities Problem Solving: Reasoning: Another Look Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. 2-6: Practice Buddy: Homework & Practice Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. End Topic Interactive Student Edition: End Topic 2 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 2 Assessment Interactive Student Edition: Topic 2 Performance Assessment Mental Math: Find Sums and Differences: Visual Learning Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Mental Math: Estimate Sums and Differences: Visual Learning Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Add Whole Numbers: Visual Learning Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 2-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Subtract Whole Numbers: Visual Learning Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Subtract Across Zeros: Visual Learning Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Problem Solving: Reasoning: Visual Learning Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Game: Factory Frenzy - Decimals Topic 2 Online Assessment Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Round greater whole numbers to estimate sums and differences. Add numbers to one million with and without regrouping using the standard algorithm. Use number sense and regrouping to subtract across zeros. Use place value and an algorithm to subtract whole numbers. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Practice Buddy: Fluency Practice/Assessment Topic 3: Use Strategies and Properties to Multiply by 1-Digit Numbers Topic 3: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 3 Math and Science Project Review What You Know Vocabulary Cards 3-1: Mental Math: Multiply by Multiples of 10, 100, and 1,000 Student's Edition eText: Grade 4 Lesson 3-1 Interactive Student Edition: Grade 4 Lesson 3-1 Student's Edition ACTIVe-book: Grade 4 Lesson 3-1 Math Anytime Mental Math: Multiply by Multiples of 10, 100, and 1,000: Review Topic 3: Today's Challenge Develop: Problem-Based Learning Mental Math: Multiply by Multiples of 10, 100, and 1,000: Solve & Share Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Develop: Visual Learning Mental Math: Multiply by Multiples of 10, 100, and 1,000: Visual Learning Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Mental Math: Multiply by Multiples of 10, 100, and 1,000: Convince Me! Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Mental Math: Multiply by Multiples of 10, 100, and 1,000: Practice Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Assess & Differentiate 3-1: Homework & Practice Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-1: Homework & Practice Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Mental Math: Multiply by Multiples of 10, 100, and 1,000: Quick Check Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-1: Reteach to Build Understanding Worksheet Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-1: Enrichment Worksheet 3-1: Center Games Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Digital Math Tool Activities Mental Math: Multiply by Multiples of 10, 100, and 1,000: Another Look Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-1: Practice Buddy: Homework & Practice Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-2: Mental Math: Round to Estimate Products Student's Edition eText: Grade 4 Lesson 3-2 Interactive Student Edition: Grade 4 Lesson 3-2 Student's Edition ACTIVe-book: Grade 4 Lesson 3-2 Math Anytime Mental Math: Round to Estimate Products: Review Topic 3: Today's Challenge Develop: Problem-Based Learning Mental Math: Round to Estimate Products: Solve & Share Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Mental Math: Round to Estimate Products: Visual Learning Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Round to Estimate Products: Convince Me! Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Round to Estimate Products: Practice Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 3-2: Homework & Practice Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-2: Homework & Practice Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Round to Estimate Products: Quick Check Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-2: Enrichment Worksheet 3-2: Center Games Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers Mental Math: Round to Estimate Products: Another Look Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-2: Practice Buddy: Homework & Practice Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-3: The Distributive Property Student's Edition eText: Grade 4 Lesson 3-3 Interactive Student Edition: Grade 4 Lesson 3-3 Student's Edition ACTIVe-book: Grade 4 Lesson 3-3 Math Anytime The Distributive Property: Review Topic 3: Today's Challenge Develop: Problem-Based Learning The Distributive Property: Solve & Share Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Develop: Visual Learning The Distributive Property: Visual Learning Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. The Distributive Property: Convince Me! Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. The Distributive Property: Practice Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Assess & Differentiate 3-3: Homework & Practice Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-3: Homework & Practice Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. The Distributive Property: Quick Check Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-3: Enrichment Worksheet 3-3: Center Games Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers The Distributive Property: Another Look Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-3: Practice Buddy: Homework & Practice Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-4: Mental Math Strategies for Multiplication Interactive Student Edition: Grade 4 Lesson 3-4 3-5: Arrays and Partial Products Interactive Student Edition: Grade 4 Lesson 3-5 3-6: Use Partial Products to Multiply by 1-Digit Numbers Interactive Student Edition: Grade 4 Lesson 3-6 3-7: Multiply 2- and 3-Digit Numbers by 1-Digit Numbers Interactive Student Edition: Grade 4 Lesson 3-7 3-8: Multiply 4-Digit by 1-Digit Numbers Interactive Student Edition: Grade 4 Lesson 3-8 3-9: Multiply by 1-Digit Numbers Interactive Student Edition: Grade 4 Lesson 3-9 3-10: Problem Solving: Model with Math Interactive Student Edition: Grade 4 Lesson 3-10 End Topic Interactive Student Edition: End Topic 3 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 3 Assessment Interactive Student Edition: Topic 3 Performance Assessment Multiply by 1-Digit Numbers: Visual Learning Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1- digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply by 1-Digit Numbers: Another Look Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1- digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Problem Solving: Model with Math: Visual Learning Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Model with mathematics. Model with mathematics. Game: Multo - 2-Digit Numbers Mental Math: Multiply by Multiples of 10, 100, and 1,000: Visual Learning Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 3-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Round to Estimate Products: Visual Learning Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. The Distributive Property: Visual Learning Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Mental Math Strategies for Multiplication: Visual Learning Curriculum Standards: Use place value and properties of operations to multiply mentally. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Arrays and Partial Products: Visual Learning Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Use Partial Products to Multiply by 1-Digit Numbers: Visual Learning Curriculum Standards: Use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2- and 3-Digit Numbers by 1-Digit Numbers: Visual Learning Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-7: Reteach to Build Understanding Worksheet Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 3-8: Reteach to Build Understanding Worksheet Curriculum Standards: Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 4-Digit by 1-Digit Numbers: Visual Learning Curriculum Standards: Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 3 Online Assessment Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Use place value and properties of operations to multiply mentally. Use the standard algorithm to multiply 2-, 3-, and 4- digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. Use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies Use rounding to estimate products and check if answers are reasonable. Use the Distributive Property to multiply larger numbers. Use previously- learned concepts and skills to represent and solve problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Model with mathematics. Model with mathematics. Topic 4: Use Strategies and Properties to Multiply by 2-Digit Numbers Topic 4: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 4 Math and Science Project Review What You Know Vocabulary Cards 4-1: Mental Math: Multiply Multiples of 10 Student's Edition eText: Grade 4 Lesson 4-1 Interactive Student Edition: Grade 4 Lesson 4-1 Student's Edition ACTIVe-book: Grade 4 Lesson 4-1 Math Anytime Mental Math: Multiply Multiples of 10: Review Topic 4: Today's Challenge Develop: Problem-Based Learning Mental Math: Multiply Multiples of 10: Solve & Share Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Mental Math: Multiply Multiples of 10: Visual Learning Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Multiply Multiples of 10: Convince Me! Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Multiply Multiples of 10: Practice Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 4-1: Homework & Practice Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-1: Homework & Practice Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Multiply Multiples of 10: Quick Check Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-1: Enrichment Worksheet 4-1: Center Games Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers Mental Math: Multiply Multiples of 10: Another Look Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-1: Practice Buddy: Homework & Practice Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-2: Use Models to Multiply 2-Digit Numbers by Multiples of 10 Interactive Student Edition: Grade 4 Lesson 4-2 4-3: Estimate: Use Rounding Student's Edition eText: Grade 4 Lesson 4-3 Interactive Student Edition: Grade 4 Lesson 4-3 Student's Edition ACTIVe-book: Grade 4 Lesson 4-3 Math Anytime Estimate: Use Rounding: Review Topic 4: Today's Challenge Develop: Problem-Based Learning Estimate: Use Rounding: Solve & Share Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Estimate: Use Rounding: Visual Learning Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Estimate: Use Rounding: Convince Me! Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Estimate: Use Rounding: Practice Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 4-3: Homework & Practice Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-3: Homework & Practice Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Estimate: Use Rounding: Quick Check Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-3: Reteach to Build Understanding Worksheet Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-3: Enrichment Worksheet 4-3: Problem-Solving Reading Activity Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Digital Math Tool Activities Estimate: Use Rounding: Another Look Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-3: Practice Buddy: Homework & Practice Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-4: Estimate: Use Compatible Numbers Student's Edition eText: Grade 4 Lesson 4-4 Interactive Student Edition: Grade 4 Lesson 4-4 Student's Edition ACTIVe-book: Grade 4 Lesson 4-4 Math Anytime Estimate: Use Compatible Numbers: Review Topic 4: Today's Challenge Develop: Problem-Based Learning Estimate: Use Compatible Numbers: Solve & Share Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Develop: Visual Learning Estimate: Use Compatible Numbers: Visual Learning Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Estimate: Use Compatible Numbers: Convince Me! Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Estimate: Use Compatible Numbers: Practice Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Assess & Differentiate 4-4: Homework & Practice Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-4: Homework & Practice Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Estimate: Use Compatible Numbers: Quick Check Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-4: Enrichment Worksheet 4-4: Center Games Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Digital Math Tool Activities Estimate: Use Compatible Numbers: Another Look Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-4: Practice Buddy: Homework & Practice Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. 4-5: Arrays and Partial Products Interactive Student Edition: Grade 4 Lesson 4-5 4-6: Multiply Using the Distributive Property Interactive Student Edition: Grade 4 Lesson 4-6 4-7: Use Partial Products to Multiply by 2-Digit Numbers Interactive Student Edition: Grade 4 Lesson 4-7 4-8: Multiply 2-Digit Numbers by Multiples of 10 Interactive Student Edition: Grade 4 Lesson 4-8 4-9: Multiply 2-Digit by 2-Digit Numbers Student's Edition eText: Grade 4 Lesson 4-9 Interactive Student Edition: Grade 4 Lesson 4-9 Student's Edition ACTIVe-book: Grade 4 Lesson 4-9 Math Anytime Multiply 2-Digit by 2-Digit Numbers: Review Topic 4: Today's Challenge Develop: Problem-Based Learning Multiply 2-Digit by 2-Digit Numbers: Solve & Share Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Multiply 2-Digit by 2-Digit Numbers: Visual Learning Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2-Digit by 2-Digit Numbers: Convince Me! Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2-Digit by 2-Digit Numbers: Practice Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 4-9: Homework & Practice Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Homework & Practice Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2-Digit by 2-Digit Numbers: Quick Check Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Reteach to Build Understanding Worksheet Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Enrichment Worksheet 4-9: Problem-Solving Reading Activity Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Multo - 2-Digit Numbers Multiply 2-Digit by 2-Digit Numbers: Another Look Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-9: Practice Buddy: Homework & Practice Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Continue to Multiply by 2-Digit Numbers Student's Edition eText: Grade 4 Lesson 4-10 Interactive Student Edition: Grade 4 Lesson 4-10 Student's Edition ACTIVe-book: Grade 4 Lesson 4-10 Math Anytime Continue to Multiply by 2-Digit Numbers: Review Topic 4: Today's Challenge Develop: Problem-Based Learning Continue to Multiply by 2-Digit Numbers: Solve & Share Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Continue to Multiply by 2-Digit Numbers: Visual Learning Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Continue to Multiply by 2-Digit Numbers: Convince Me! Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Continue to Multiply by 2-Digit Numbers: Practice Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 4-10: Homework & Practice Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Homework & Practice Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Continue to Multiply by 2-Digit Numbers: Quick Check Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Reteach to Build Understanding Worksheet Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Enrichment Worksheet 4-10: Math and Science Activity Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Multo - 2-Digit Numbers Continue to Multiply by 2-Digit Numbers: Another Look Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-10: Practice Buddy: Homework & Practice Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-11: Problem Solving: Make Sense & Persevere Interactive Student Edition: Grade 4 Lesson 4-11 End Topic Interactive Student Edition: End Topic 4 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 4 Assessment Interactive Student Edition: Topic 4 Performance Assessment 5-5: Center Games Mental Math: Multiply Multiples of 10: Visual Learning Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Models to Multiply 2-Digit Numbers by Multiples of 10: Visual Learning Curriculum Standards: Use models and properties of operations to multiply 2-digit numbers by multiples of ten. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Estimate: Use Rounding: Visual Learning Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Estimate: Use Compatible Numbers: Visual Learning Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Arrays and Partial Products: Visual Learning Curriculum Standards: Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply Using the Distributive Property: Visual Learning Curriculum Standards: Use the Distributive Property and an area model to multiply two 2-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Use Partial Products to Multiply by 2-Digit Numbers: Visual Learning Curriculum Standards: Use place value and partial products to calculate products of 2-digit by 2- digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2-Digit Numbers by Multiples of 10: Visual Learning Curriculum Standards: Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3- digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one- digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 4-8: Reteach to Build Understanding Worksheet Curriculum Standards: Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3- digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one- digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2-Digit by 2-Digit Numbers: Visual Learning Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Continue to Multiply by 2-Digit Numbers: Visual Learning Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Problem Solving: Make Sense & Persevere: Visual Learning Curriculum Standards: Make sense of problems and persevere in solving them. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Topic 4 Online Assessment Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Use the Distributive Property and an area model to multiply two 2-digit numbers. Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. Make sense of problems and persevere in solving them. Use the expanded and the standard algorithm to multiply 2- digit by 2-digit numbers. Estimate to check if products are reasonable. Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Use models and properties of operations to multiply 2- digit numbers by multiples of ten. Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Multiply 2-Digit by 2-Digit Numbers: Visual Learning Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Continue to Multiply by 2-Digit Numbers: Visual Learning Curriculum Standards: Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Problem Solving: Make Sense & Persevere: Visual Learning Curriculum Standards: Make sense of problems and persevere in solving them. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 5-1: Center Games G13: Estimating Sums and Differences of Greater Numbers Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G18: Adding Greater Numbers Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Numbers Through One Million: Visual Learning Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Place Value Relationships: Visual Learning Curriculum Standards: Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. Compare Whole Numbers: Visual Learning Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Round Whole Numbers: Visual Learning Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. Mental Math: Find Sums and Differences: Visual Learning Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Mental Math: Estimate Sums and Differences: Visual Learning Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Add Whole Numbers: Visual Learning Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Subtract Whole Numbers: Visual Learning Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Problem Solving: Reasoning: Visual Learning Curriculum Standards: Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Mental Math: Multiply by Multiples of 10, 100, and 1,000: Visual Learning Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Mental Math: Round to Estimate Products: Visual Learning Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. The Distributive Property: Visual Learning Curriculum Standards: Use the Distributive Property to multiply larger numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Mental Math Strategies for Multiplication: Visual Learning Curriculum Standards: Use place value and properties of operations to multiply mentally. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2- digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. G42: Estimating Products Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G47: Multiplying Three-Digit Numbers Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G46: Multiplying Two-Digit Numbers Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1- digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G65: Estimating Products Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Arrays and Partial Products: Visual Learning Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply 2- and 3-Digit Numbers by 1-Digit Numbers: Visual Learning Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 4-Digit by 1-Digit Numbers: Visual Learning Curriculum Standards: Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2- digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply by 1-Digit Numbers: Visual Learning Curriculum Standards: Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1- digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Estimate: Use Rounding: Visual Learning Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Estimate: Use Compatible Numbers: Visual Learning Curriculum Standards: Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Use Partial Products to Multiply by 2-Digit Numbers: Visual Learning Curriculum Standards: Use place value and partial products to calculate products of 2-digit by 2- digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topics 1–4: Online Cumulative/Benchmark Assessment Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Model with mathematics. Look for and make use of structure. Make sense of problems and persevere in solving them. Use rounding to estimate products and check if answers are reasonable. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Reason abstractly and quantitatively. Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Round greater whole numbers to estimate sums and differences. Use place value and an algorithm to subtract whole numbers. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. Recognize the relationship between adjacent digits in a multi-digit number. Use place value to compare multi-digit numbers. Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Add and subtract whole numbers mentally using a variety of methods. Use the Distributive Property to multiply larger numbers. Use place value to round multi-digit numbers. Read and write numbers in expanded form, with numerals, and using number names. Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. Add numbers to one million with and without regrouping using the standard algorithm. Use place value and properties of operations to multiply mentally. Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1- digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Model with mathematics. Model with mathematics. Look for and make use of structure. Look for and make use of structure. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. Use estimation strategies to assess reasonableness of answers. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Represent problems using equations with a letter standing for the unknown quantity. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base- ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Round multi-digit whole numbers to any place. Topic 5: Use Strategies and Properties to Divide by 1-Digit Numbers Topic 5: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 5 Math and Science Project Review What You Know Vocabulary Cards 5-1: Mental Math: Find Quotients Student's Edition eText: Grade 4 Lesson 5-1 Interactive Student Edition: Grade 4 Lesson 5-1 Student's Edition ACTIVe-book: Grade 4 Lesson 5-1 Math Anytime Mental Math: Find Quotients: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Mental Math: Find Quotients: Solve & Share Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Develop: Visual Learning Mental Math: Find Quotients: Visual Learning Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Find Quotients: Convince Me! Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Find Quotients: Practice Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Assess & Differentiate 5-1: Homework & Practice Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-1: Homework & Practice Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Find Quotients: Quick Check Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-1: Enrichment Worksheet 5-1: Center Games Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Find Quotients: Another Look Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-1: Practice Buddy: Homework & Practice Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Mental Math: Estimate Quotients Student's Edition eText: Grade 4 Lesson 5-2 Interactive Student Edition: Grade 4 Lesson 5-2 Student's Edition ACTIVe-book: Grade 4 Lesson 5-2 Math Anytime Mental Math: Estimate Quotients: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Mental Math: Estimate Quotients: Solve & Share Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Develop: Visual Learning Mental Math: Estimate Quotients: Visual Learning Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients: Convince Me! Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients: Practice Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Assess & Differentiate 5-2: Homework & Practice Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Homework & Practice Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients: Quick Check Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Enrichment Worksheet 5-2: Center Games Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Estimate Quotients: Another Look Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-2: Practice Buddy: Homework & Practice Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Mental Math: Estimate Quotients for Greater Dividends Student's Edition eText: Grade 4 Lesson 5-3 Interactive Student Edition: Grade 4 Lesson 5-3 Student's Edition ACTIVe-book: Grade 4 Lesson 5-3 Math Anytime Mental Math: Estimate Quotients for Greater Dividends: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Mental Math: Estimate Quotients for Greater Dividends: Solve & Share Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Develop: Visual Learning Mental Math: Estimate Quotients for Greater Dividends: Visual Learning Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients for Greater Dividends: Convince Me! Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients for Greater Dividends: Practice Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Assess & Differentiate 5-3: Homework & Practice Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Homework & Practice Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients for Greater Dividends: Quick Check Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Enrichment Worksheet 5-3: Math and Science Activity Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Estimate Quotients for Greater Dividends: Another Look Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-3: Practice Buddy: Homework & Practice Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Interpret Remainders Student's Edition eText: Grade 4 Lesson 5-4 Interactive Student Edition: Grade 4 Lesson 5-4 Student's Edition ACTIVe-book: Grade 4 Lesson 5-4 Math Anytime Interpret Remainders: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Interpret Remainders: Solve & Share Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Develop: Visual Learning Interpret Remainders: Visual Learning Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Interpret Remainders: Convince Me! Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Interpret Remainders: Practice Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Assess & Differentiate 5-4: Homework & Practice Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Homework & Practice Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Interpret Remainders: Quick Check Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Enrichment Worksheet 5-4: Center Games Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Digital Math Tool Activities Interpret Remainders: Another Look Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-4: Practice Buddy: Homework & Practice Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. 5-5: Division as Sharing Student's Edition eText: Grade 4 Lesson 5-5 Interactive Student Edition: Grade 4 Lesson 5-5 Student's Edition ACTIVe-book: Grade 4 Lesson 5-5 Math Anytime Division as Sharing: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Division as Sharing: Solve & Share Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Division as Sharing: Visual Learning Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Division as Sharing: Convince Me! Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Division as Sharing: Practice Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 5-5: Homework & Practice Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Homework & Practice Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Division as Sharing: Quick Check Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Enrichment Worksheet 5-5: Center Games Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Digital Math Tool Activities Division as Sharing: Another Look Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Practice Buddy: Homework & Practice Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1- digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Use Partial Quotients to Divide Student's Edition eText: Grade 4 Lesson 5-6 Interactive Student Edition: Grade 4 Lesson 5-6 Student's Edition ACTIVe-book: Grade 4 Lesson 5-6 Math Anytime Use Partial Quotients to Divide: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Use Partial Quotients to Divide: Solve & Share Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Use Partial Quotients to Divide: Visual Learning Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Convince Me! Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Practice Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 5-6: Homework & Practice Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Homework & Practice Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Quick Check Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Enrichment Worksheet 5-6: Problem-Solving Reading Activity Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Use Partial Quotients to Divide: Another Look Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-6: Practice Buddy: Homework & Practice Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Use Partial Quotients to Divide: Greater Dividends Student's Edition eText: Grade 4 Lesson 5-7 Interactive Student Edition: Grade 4 Lesson 5-7 Student's Edition ACTIVe-book: Grade 4 Lesson 5-7 Math Anytime Use Partial Quotients to Divide: Greater Dividends: Review Topic 5: Today's Challenge Develop: Problem-Based Learning Use Partial Quotients to Divide: Greater Dividends: Solve & Share Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Develop: Visual Learning Use Partial Quotients to Divide: Greater Dividends: Visual Learning Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Greater Dividends: Convince Me! Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Greater Dividends: Practice Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Assess & Differentiate 5-7: Homework & Practice Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Homework & Practice Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Greater Dividends: Quick Check Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Reteach to Build Understanding Worksheet Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Enrichment Worksheet 5-7: Math and Science Activity Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Digital Math Tool Activities Use Partial Quotients to Divide: Greater Dividends: Another Look Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-7: Practice Buddy: Homework & Practice Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-8: Divide with 1-Digit Numbers Interactive Student Edition: Grade 4 Lesson 5-8 5-9: Continue to Divide with 1-Digit Numbers Interactive Student Edition: Grade 4 Lesson 5-9 5-10: Problem Solving: Model With Math Interactive Student Edition: Grade 4 Lesson 5-10 End Topic Interactive Student Edition: End Topic 5 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 5 Assessment Interactive Student Edition: Topic 5 Performance Assessment Division as Sharing: Visual Learning Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. 5-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Visual Learning Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Use Partial Quotients to Divide: Greater Dividends: Visual Learning Curriculum Standards: Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Divide with 1-Digit Numbers: Visual Learning Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Continue to Divide with 1-Digit Numbers: Visual Learning Curriculum Standards: Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Find Quotients: Visual Learning Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers Mental Math: Estimate Quotients: Visual Learning Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Mental Math: Estimate Quotients for Greater Dividends: Visual Learning Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4- digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Interpret Remainders: Visual Learning Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Topic 5 Online Assessment Curriculum Standards: Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Use compatible numbers to estimate quotients. Solve division problems and interpret remainders. Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. Use partial quotients and place-value understandings to divide with greater dividends. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Interpret remainders in word problems. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topic 6: Use Operations with Whole Numbers to Solve Problems Topic 6: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 6 Math and Science Project Review What You Know 6-1: Solve Comparison Situations Student's Edition eText: Grade 4 Lesson 6-1 Interactive Student Edition: Grade 4 Lesson 6-1 Student's Edition ACTIVe-book: Grade 4 Lesson 6-1 Math Anytime Solve Comparison Situations: Review Topic 6: Today's Challenge Develop: Problem-Based Learning Solve Comparison Situations: Solve & Share Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Develop: Visual Learning Solve Comparison Situations: Visual Learning Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve Comparison Situations: Convince Me! Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve Comparison Situations: Practice Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Assess & Differentiate 6-1: Homework & Practice Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-1: Homework & Practice Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve Comparison Situations: Quick Check Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-1: Reteach to Build Understanding Worksheet Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-1: Enrichment Worksheet 6-1: Problem-Solving Reading Activity Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Digital Math Tool Activities Solve Comparison Situations: Another Look Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-1: Practice Buddy: Homework & Practice Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. 6-2: Continue to Solve Comparison Situations Interactive Student Edition: Grade 4 Lesson 6-2 6-3: Solve Multi-Step Problems Student's Edition eText: Grade 4 Lesson 6-3 Interactive Student Edition: Grade 4 Lesson 6-3 Student's Edition ACTIVe-book: Grade 4 Lesson 6-3 Math Anytime Solve Multi-Step Problems: Review Topic 6: Today's Challenge Develop: Problem-Based Learning Solve Multi-Step Problems: Solve & Share Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Develop: Visual Learning Solve Multi-Step Problems: Visual Learning Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Solve Multi-Step Problems: Convince Me! Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Solve Multi-Step Problems: Practice Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Assess & Differentiate 6-3: Homework & Practice Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-3: Homework & Practice Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Solve Multi-Step Problems: Quick Check Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-3: Enrichment Worksheet 6-3: Math and Science Activity Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Solve Multi-Step Problems: Another Look Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-3: Practice Buddy: Homework & Practice Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Solve More Multi-Step Problems Student's Edition eText: Grade 4 Lesson 6-4 Interactive Student Edition: Grade 4 Lesson 6-4 Student's Edition ACTIVe-book: Grade 4 Lesson 6-4 Math Anytime Solve More Multi-Step Problems: Review Topic 6: Today's Challenge Develop: Problem-Based Learning Solve More Multi-Step Problems: Solve & Share Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Develop: Visual Learning Solve More Multi-Step Problems: Visual Learning Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Solve More Multi-Step Problems: Convince Me! Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Solve More Multi-Step Problems: Practice Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Assess & Differentiate 6-4: Homework & Practice Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Homework & Practice Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Solve More Multi-Step Problems: Quick Check Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Enrichment Worksheet 6-4: Math and Science Activity Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Solve More Multi-Step Problems: Another Look Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Practice Buddy: Homework & Practice Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-5: Problem Solving: Make Sense & Persevere Interactive Student Edition: Grade 4 Lesson 6-5 End Topic Interactive Student Edition: End Topic 6 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 6 Assessment Interactive Student Edition: Topic 6 Performance Assessment Problem Solving: Make Sense & Persevere: Visual Learning Curriculum Standards: Make sense of a multi-step problem and keep working until it is solved. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Solve Comparison Situations: Visual Learning Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Continue to Solve Comparison Situations: Another Look Curriculum Standards: Use multiplication and division to compare two quantities. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve Multi-Step Problems: Visual Learning Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 6-1: Reteach to Build Understanding Worksheet Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Continue to Solve Comparison Situations: Visual Learning Curriculum Standards: Use multiplication and division to compare two quantities. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve More Multi-Step Problems: Visual Learning Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. 7-4: Center Games Topic 6 Online Assessment Curriculum Standards: Interpret comparisons as multiplication or addition equations. Make sense of a multi-step problem and keep working until it is solved. Solve two-step problems by finding and solving the hidden question first. Use multiplication and division to compare two quantities. Solve multi-step problems by finding and solving hidden questions first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real- world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Topic 7: Factors and Multiples Topic 7: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 7 Math and Science Project Review What You Know Vocabulary Cards 7-1: Understand Factors Student's Edition eText: Grade 4 Lesson 7-1 Interactive Student Edition: Grade 4 Lesson 7-1 Student's Edition ACTIVe-book: Grade 4 Lesson 7-1 Math Anytime Understand Factors: Review Topic 7: Today's Challenge Develop: Problem-Based Learning Understand Factors: Solve & Share Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Develop: Visual Learning Understand Factors: Visual Learning Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Understand Factors: Convince Me! Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Understand Factors: Practice Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Assess & Differentiate 7-1: Homework & Practice Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-1: Homework & Practice Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Understand Factors: Quick Check Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-1: Enrichment Worksheet 7-1: Math and Science Activity Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Digital Math Tool Activities Understand Factors: Another Look Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-1: Practice Buddy: Homework & Practice Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Factors Student's Edition eText: Grade 4 Lesson 7-2 Interactive Student Edition: Grade 4 Lesson 7-2 Student's Edition ACTIVe-book: Grade 4 Lesson 7-2 Math Anytime Factors: Review Topic 7: Today's Challenge Develop: Problem-Based Learning Factors: Solve & Share Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Develop: Visual Learning Factors: Visual Learning Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Factors: Convince Me! Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Factors: Practice Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Assess & Differentiate 7-2: Homework & Practice Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Homework & Practice Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Factors: Quick Check Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Enrichment Worksheet 7-2: Problem-Solving Reading Activity Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Digital Math Tool Activities Factors: Another Look Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-2: Practice Buddy: Homework & Practice Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-3: Problem Solving: Repeated Reasoning Student's Edition eText: Grade 4 Lesson 7-3 Interactive Student Edition: Grade 4 Lesson 7-3 Student's Edition ACTIVe-book: Grade 4 Lesson 7-3 Math Anytime Problem Solving: Repeated Reasoning: Review Topic 7: Today's Challenge Develop: Problem-Based Learning Problem Solving: Repeated Reasoning: Solve & Share Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Develop: Visual Learning Problem Solving: Repeated Reasoning: Visual Learning Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Problem Solving: Repeated Reasoning: Convince Me! Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Problem Solving: Repeated Reasoning: Practice Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Assess & Differentiate 7-3: Homework & Practice Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-3: Homework & Practice Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Problem Solving: Repeated Reasoning: Quick Check Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-3: Enrichment Worksheet 7-3: Math and Science Activity Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Digital Math Tool Activities Problem Solving: Repeated Reasoning: Another Look Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-3: Practice Buddy: Homework & Practice Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. 7-4: Prime and Composite Numbers Student's Edition eText: Grade 4 Lesson 7-4 Interactive Student Edition: Grade 4 Lesson 7-4 Student's Edition ACTIVe-book: Grade 4 Lesson 7-4 Math Anytime Prime and Composite Numbers: Review Topic 7: Today's Challenge Develop: Problem-Based Learning Prime and Composite Numbers: Solve & Share Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Develop: Visual Learning Prime and Composite Numbers: Visual Learning Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Prime and Composite Numbers: Convince Me! Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Prime and Composite Numbers: Practice Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Assess & Differentiate 7-4: Homework & Practice Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-4: Homework & Practice Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Prime and Composite Numbers: Quick Check Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-4: Enrichment Worksheet 7-4: Center Games Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Digital Math Tool Activities Prime and Composite Numbers: Another Look Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-4: Practice Buddy: Homework & Practice Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Multiples Student's Edition eText: Grade 4 Lesson 7-5 Interactive Student Edition: Grade 4 Lesson 7-5 Student's Edition ACTIVe-book: Grade 4 Lesson 7-5 Math Anytime Multiples: Review Topic 7: Today's Challenge Develop: Problem-Based Learning Multiples: Solve & Share Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Develop: Visual Learning Multiples: Visual Learning Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Multiples: Convince Me! Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Multiples: Practice Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Assess & Differentiate 7-5: Homework & Practice Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Homework & Practice Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Multiples: Quick Check Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Enrichment Worksheet 7-5: Problem-Solving Reading Activity Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Game: Save the Word: Grade 4 Topics 1–4 Multiples: Another Look Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 7-5: Practice Buddy: Homework & Practice Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. End Topic Interactive Student Edition: End Topic 7 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 7 Assessment Interactive Student Edition: Topic 7 Performance Assessment Multiples: Visual Learning Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Understand Factors: Visual Learning Curriculum Standards: Use arrays to find the factors of a given whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Factors: Visual Learning Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one- digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Problem Solving: Repeated Reasoning: Visual Learning Curriculum Standards: Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Prime and Composite Numbers: Visual Learning Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. 8-1: Center Games Topic 7 Online Assessment Curriculum Standards: Use arrays to find the factors of a given whole number. Use repeated reasoning to generalize how to solve problems that are similar. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Topic 8: Extend Understanding of Fraction Equivalence and Ordering Topic 8: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 8 Math and Science Project Review What You Know Vocabulary Cards 8-1: Equivalent Fractions: Area Models Student's Edition eText: Grade 4 Lesson 8-1 Interactive Student Edition: Grade 4 Lesson 8-1 Student's Edition ACTIVe-book: Grade 4 Lesson 8-1 Math Anytime Equivalent Fractions: Area Models: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Equivalent Fractions: Area Models: Solve & Share Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Develop: Visual Learning Equivalent Fractions: Area Models: Visual Learning Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Area Models: Convince Me! Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Area Models: Practice Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Assess & Differentiate 8-1: Homework & Practice Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-1: Homework & Practice Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Area Models: Quick Check Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-1: Enrichment Worksheet 8-1: Center Games Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Digital Math Tool Activities Equivalent Fractions: Area Models: Another Look Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-1: Practice Buddy: Homework & Practice Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Equivalent Fractions: Number Lines Student's Edition eText: Grade 4 Lesson 8-2 Interactive Student Edition: Grade 4 Lesson 8-2 Student's Edition ACTIVe-book: Grade 4 Lesson 8-2 Math Anytime Equivalent Fractions: Number Lines: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Equivalent Fractions: Number Lines: Solve & Share Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Develop: Visual Learning Equivalent Fractions: Number Lines: Visual Learning Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Number Lines: Convince Me! Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Number Lines: Practice Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Assess & Differentiate 8-2: Homework & Practice Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Homework & Practice Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Number Lines: Quick Check Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Enrichment Worksheet 8-2: Center Games Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Digital Math Tool Activities Equivalent Fractions: Number Lines: Another Look Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-2: Practice Buddy: Homework & Practice Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Generate Equivalent Fractions: Multiplication Student's Edition eText: Grade 4 Lesson 8-3 Interactive Student Edition: Grade 4 Lesson 8-3 Student's Edition ACTIVe-book: Grade 4 Lesson 8-3 Math Anytime Generate Equivalent Fractions: Multiplication: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Generate Equivalent Fractions: Multiplication: Solve & Share Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Develop: Visual Learning Generate Equivalent Fractions: Multiplication: Visual Learning Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Multiplication: Convince Me! Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Multiplication: Practice Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Assess & Differentiate 8-3: Homework & Practice Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Homework & Practice Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Multiplication: Quick Check Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Enrichment Worksheet 8-3: Center Games Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Digital Math Tool Activities Generate Equivalent Fractions: Multiplication: Another Look Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-3: Practice Buddy: Homework & Practice Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. 8-4: Generate Equivalent Fractions: Division Student's Edition eText: Grade 4 Lesson 8-4 Interactive Student Edition: Grade 4 Lesson 8-4 Student's Edition ACTIVe-book: Grade 4 Lesson 8-4 Math Anytime Generate Equivalent Fractions: Division: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Generate Equivalent Fractions: Division: Solve & Share Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Develop: Visual Learning Generate Equivalent Fractions: Division: Visual Learning Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Division: Convince Me! Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Division: Practice Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Assess & Differentiate 8-4: Homework & Practice Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-4: Homework & Practice Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Division: Quick Check Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-4: Enrichment Worksheet 8-4: Problem-Solving Reading Activity Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Digital Math Tool Activities Generate Equivalent Fractions: Division: Another Look Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-4: Practice Buddy: Homework & Practice Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. 8-5: Use Benchmarks to Compare Fractions Student's Edition eText: Grade 4 Lesson 8-5 Interactive Student Edition: Grade 4 Lesson 8-5 Student's Edition ACTIVe-book: Grade 4 Lesson 8-5 Math Anytime Use Benchmarks to Compare Fractions: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Use Benchmarks to Compare Fractions: Solve & Share Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Develop: Visual Learning Use Benchmarks to Compare Fractions: Visual Learning Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Use Benchmarks to Compare Fractions: Convince Me! Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Use Benchmarks to Compare Fractions: Practice Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Assess & Differentiate 8-5: Homework & Practice Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-5: Homework & Practice Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Use Benchmarks to Compare Fractions: Quick Check Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-5: Enrichment Worksheet 8-5: Math and Science Activity Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Use Benchmarks to Compare Fractions: Another Look Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-5: Practice Buddy: Homework & Practice Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Compare Fractions Student's Edition eText: Grade 4 Lesson 8-6 Interactive Student Edition: Grade 4 Lesson 8-6 Student's Edition ACTIVe-book: Grade 4 Lesson 8-6 Math Anytime Compare Fractions: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Compare Fractions: Solve & Share Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Develop: Visual Learning Compare Fractions: Visual Learning Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Compare Fractions: Convince Me! Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Compare Fractions: Practice Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Assess & Differentiate 8-6: Homework & Practice Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Homework & Practice Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Compare Fractions: Quick Check Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Enrichment Worksheet 8-6: Math and Science Activity Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Compare Fractions: Another Look Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Practice Buddy: Homework & Practice Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-7: Problem Solving: Construct Arguments Student's Edition eText: Grade 4 Lesson 8-7 Interactive Student Edition: Grade 4 Lesson 8-7 Student's Edition ACTIVe-book: Grade 4 Lesson 8-7 Math Anytime Problem Solving: Construct Arguments: Review Topic 8: Today's Challenge Develop: Problem-Based Learning Problem Solving: Construct Arguments: Solve & Share Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Develop: Visual Learning Problem Solving: Construct Arguments: Visual Learning Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Construct Arguments: Convince Me! Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Construct Arguments: Practice Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 8-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Assess & Differentiate 8-7: Homework & Practice Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 8-7: Homework & Practice Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Construct Arguments: Quick Check Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 8-7: Reteach to Build Understanding Worksheet Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 8-7: Enrichment Worksheet 8-7: Problem-Solving Reading Activity Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Game: Save the Word: Grade 4 Topics 1–8 Problem Solving: Construct Arguments: Another Look Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 8-7: Practice Buddy: Homework & Practice Curriculum Standards: Construct arguments about fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will compare and order fractions and mixed numbers, with and without models. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. End Topic Interactive Student Edition: End Topic 8 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 8 Assessment Interactive Student Edition: Topic 8 Performance Assessment Game: Jungle Quest - Equivalent Fractions Generate Equivalent Fractions: Multiplication: Visual Learning Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Division: Visual Learning Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Equivalent Fractions: Area Models: Visual Learning Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Equivalent Fractions: Number Lines: Visual Learning Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Use Benchmarks to Compare Fractions: Visual Learning Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. 8-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Compare Fractions: Visual Learning Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Topic 8 Online Assessment Curriculum Standards: Use division to find equivalent fractions. Use multiplication to find equivalent fractions. Use models or rename fractions to compare. Use a number line to locate and identify equivalent fractions. Use area models to recognize and generate equivalent fractions. Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Explain and/or illustrate why two fractions are equivalent. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Compare two fractions using the symbols >, = or <, and justify the solution. G43: Estimating Quotients Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve Multi-Step Problems: Visual Learning Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. Factors: Visual Learning Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one- digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Prime and Composite Numbers: Visual Learning Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Equivalent Fractions: Area Models: Visual Learning Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Multiplication: Visual Learning Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Game: Fancy Flea - Fractions F11: Comparing and Ordering Numbers Through Thousands Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. F12: Place Value Through Millions Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. G7: Adding Two-Digit Numbers Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. G16: Subtracting Across Zero Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve Comparison Situations: Visual Learning Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. G18: Adding Greater Numbers Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G21: Arrays and Multiplication Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. G24: Multiplying by 2 and 5 Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. G45: Breaking Apart Numbers to Multiply Curriculum Standards: Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G51: Interpret the Remainder Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. G53: Dividing Two-Digit Numbers Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Numbers Through One Million: Visual Learning Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare Whole Numbers: Visual Learning Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. Add Whole Numbers: Visual Learning Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G54: Dividing Three-Digit Numbers Curriculum Standards: Make sense of a multi-step problem and keep working until it is solved. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. G57: Factoring Numbers Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. G64: Mental Math: Multiplying by Multiples of 10 Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G68: Multiplying by Two-Digit Numbers Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. H9: Using Models to Find Equivalent Fractions Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Subtract Whole Numbers: Visual Learning Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi- step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Arrays and Partial Products: Visual Learning Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1- digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. H11: Comparing Fractions Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. H83: Equivalent Fractions and the Number Line Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Multiply 2- and 3-Digit Numbers by 1-Digit Numbers: Visual Learning Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Arrays and Partial Products: Visual Learning Curriculum Standards: Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply 2-Digit by 2-Digit Numbers: Visual Learning Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Estimate Quotients: Visual Learning Curriculum Standards: Use compatible numbers to estimate quotients. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Use Partial Quotients to Divide: Visual Learning Curriculum Standards: Use partial quotients to divide. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G46: Multiplying Two-Digit Numbers Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G65: Estimating Products Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. H16: Equivalent Fractions Curriculum Standards: Use multiplication to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Mental Math: Estimate Sums and Differences: Visual Learning Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Round to Estimate Products: Visual Learning Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Multiply Multiples of 10: Visual Learning Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Mental Math: Estimate Quotients for Greater Dividends: Visual Learning Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Divide with 1-Digit Numbers: Visual Learning Curriculum Standards: Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two- digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Continue to Divide with 1-Digit Numbers: Visual Learning Curriculum Standards: Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Continue to Solve Comparison Situations: Visual Learning Curriculum Standards: Use multiplication and division to compare two quantities. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Problem Solving: Make Sense & Persevere: Visual Learning Curriculum Standards: Make sense of a multi-step problem and keep working until it is solved. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Multiples: Visual Learning Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Equivalent Fractions: Number Lines: Visual Learning Curriculum Standards: Use a number line to locate and identify equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Compare Fractions: Visual Learning Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Use Benchmarks to Compare Fractions: Visual Learning Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. F7: Comparing and Ordering Numbers Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G13: Estimating Sums and Differences of Greater Numbers Curriculum Standards: Round greater whole numbers to estimate sums and differences. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Topics 1–8: Online Cumulative/Benchmark Assessment Curriculum Standards: Use appropriate tools strategically. Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use rounding to estimate products and check if answers are reasonable. Use partial quotients to divide. Use models or rename fractions to compare. Reason abstractly and quantitatively. Round greater whole numbers to estimate sums and differences. Use multiplication and division to compare two quantities. Use place value and an algorithm to subtract whole numbers. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Use place value to compare multi-digit numbers. Interpret comparisons as multiplication or addition equations. Read and write numbers in expanded form, with numerals, and using number names. Use benchmarks, area models, and number lines to compare fractions. Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Make sense of a multi-step problem and keep working until it is solved. Use multiplication to find equivalent fractions. Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Add numbers to one million with and without regrouping using the standard algorithm. Use compatible numbers to estimate quotients. Use a number line to locate and identify equivalent fractions. Use multiplication to find all the factor pairs for a whole number. Use area models to recognize and generate equivalent fractions. Use appropriate tools strategically. Use appropriate tools strategically. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2- digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Look for and make use of structure. Look for and make use of structure. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply or divide to solve problems involving a multiplicative comparison. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain and/or illustrate why two fractions are equivalent. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Topic 9: Understand Addition and Subtraction of Fractions Topic 9: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 9 Math and Science Project Review What You Know Vocabulary Cards 9-1: Model Addition of Fractions Student's Edition eText: Grade 4 Lesson 9-1 Interactive Student Edition: Grade 4 Lesson 9-1 Student's Edition ACTIVe-book: Grade 4 Lesson 9-1 Math Anytime Model Addition of Fractions: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Model Addition of Fractions: Solve & Share Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Model Addition of Fractions: Visual Learning Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Addition of Fractions: Convince Me! Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Addition of Fractions: Practice Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-1: Homework & Practice Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-1: Homework & Practice Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Addition of Fractions: Quick Check Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-1: Enrichment Worksheet 9-1: Center Games Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Fancy Flea - Fractions Model Addition of Fractions: Another Look Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-1: Practice Buddy: Homework & Practice Curriculum Standards: Use fraction strips and number lines to add fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Decompose Fractions Student's Edition eText: Grade 4 Lesson 9-2 Interactive Student Edition: Grade 4 Lesson 9-2 Student's Edition ACTIVe-book: Grade 4 Lesson 9-2 Math Anytime Decompose Fractions: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Decompose Fractions: Solve & Share Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Decompose Fractions: Visual Learning Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Decompose Fractions: Convince Me! Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Decompose Fractions: Practice Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-2: Homework & Practice Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Homework & Practice Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Decompose Fractions: Quick Check Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Reteach to Build Understanding Worksheet Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Enrichment Worksheet 9-2: Math and Science Activity Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Decompose Fractions: Another Look Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-2: Practice Buddy: Homework & Practice Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Add Fractions with Like Denominators Student's Edition eText: Grade 4 Lesson 9-3 Interactive Student Edition: Grade 4 Lesson 9-3 Student's Edition ACTIVe-book: Grade 4 Lesson 9-3 Math Anytime Add Fractions with Like Denominators: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Add Fractions with Like Denominators: Solve & Share Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Add Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Like Denominators: Convince Me! Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Like Denominators: Practice Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-3: Homework & Practice Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Homework & Practice Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Like Denominators: Quick Check Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Enrichment Worksheet 9-3: Center Games Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Fancy Flea - Fractions Add Fractions with Like Denominators: Another Look Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-3: Practice Buddy: Homework & Practice Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Model Subtraction of Fractions Student's Edition eText: Grade 4 Lesson 9-4 Interactive Student Edition: Grade 4 Lesson 9-4 Student's Edition ACTIVe-book: Grade 4 Lesson 9-4 Math Anytime Model Subtraction of Fractions: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Model Subtraction of Fractions: Solve & Share Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Model Subtraction of Fractions: Visual Learning Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Subtraction of Fractions: Convince Me! Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Subtraction of Fractions: Practice Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-4: Homework & Practice Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Homework & Practice Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Subtraction of Fractions: Quick Check Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Enrichment Worksheet 9-4: Center Games Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Model Subtraction of Fractions: Another Look Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-4: Practice Buddy: Homework & Practice Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Subtract Fractions with Like Denominators Student's Edition eText: Grade 4 Lesson 9-5 Interactive Student Edition: Grade 4 Lesson 9-5 Student's Edition ACTIVe-book: Grade 4 Lesson 9-5 Math Anytime Subtract Fractions with Like Denominators: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Subtract Fractions with Like Denominators: Solve & Share Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Fractions with Like Denominators: Convince Me! Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Fractions with Like Denominators: Practice Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-5: Homework & Practice Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Homework & Practice Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Fractions with Like Denominators: Quick Check Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Enrichment Worksheet 9-5: Center Games Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Gem Quest - Fractions Subtract Fractions with Like Denominators: Another Look Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Practice Buddy: Homework & Practice Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Add and Subtract Fractions with Like Denominators Student's Edition eText: Grade 4 Lesson 9-6 Interactive Student Edition: Grade 4 Lesson 9-6 Student's Edition ACTIVe-book: Grade 4 Lesson 9-6 Math Anytime Add and Subtract Fractions with Like Denominators: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Add and Subtract Fractions with Like Denominators: Solve & Share Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Add and Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add and Subtract Fractions with Like Denominators: Convince Me! Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add and Subtract Fractions with Like Denominators: Practice Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-6: Homework & Practice Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Homework & Practice Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add and Subtract Fractions with Like Denominators: Quick Check Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Reteach to Build Understanding Worksheet Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Enrichment Worksheet 9-6: Problem-Solving Reading Activity Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Game: Flying Cow Incident - 2-Digit Numbers Add and Subtract Fractions with Like Denominators: Another Look Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-6: Practice Buddy: Homework & Practice Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-7: Estimate Fraction Sums and Differences Student's Edition eText: Grade 4 Lesson 9-7 Interactive Student Edition: Grade 4 Lesson 9-7 Student's Edition ACTIVe-book: Grade 4 Lesson 9-7 Math Anytime Estimate Fraction Sums and Differences: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Estimate Fraction Sums and Differences: Solve & Share Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Develop: Visual Learning Estimate Fraction Sums and Differences: Visual Learning Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Estimate Fraction Sums and Differences: Convince Me! Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Estimate Fraction Sums and Differences: Practice Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Assess & Differentiate 9-7: Homework & Practice Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-7: Homework & Practice Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Estimate Fraction Sums and Differences: Quick Check Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-7: Reteach to Build Understanding Worksheet Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-7: Enrichment Worksheet 9-7: Math and Science Activity Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Game: Fancy Flea - Fractions Estimate Fraction Sums and Differences: Another Look Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-7: Practice Buddy: Homework & Practice Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. 9-8: Model Addition and Subtraction of Mixed Numbers Student's Edition eText: Grade 4 Lesson 9-8 Interactive Student Edition: Grade 4 Lesson 9-8 Student's Edition ACTIVe-book: Grade 4 Lesson 9-8 Math Anytime Model Addition and Subtraction of Mixed Numbers: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Model Addition and Subtraction of Mixed Numbers: Solve & Share Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Model Addition and Subtraction of Mixed Numbers: Visual Learning Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Addition and Subtraction of Mixed Numbers: Convince Me! Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Addition and Subtraction of Mixed Numbers: Practice Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-8: Homework & Practice Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-8: Homework & Practice Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Addition and Subtraction of Mixed Numbers: Quick Check Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-8: Reteach to Build Understanding Worksheet Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-8: Enrichment Worksheet 9-8: Center Games Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Model Addition and Subtraction of Mixed Numbers: Another Look Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-8: Practice Buddy: Homework & Practice Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Add Mixed Numbers Student's Edition eText: Grade 4 Lesson 9-9 Interactive Student Edition: Grade 4 Lesson 9-9 Student's Edition ACTIVe-book: Grade 4 Lesson 9-9 Math Anytime Add Mixed Numbers: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Add Mixed Numbers: Solve & Share Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Add Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Mixed Numbers: Convince Me! Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Mixed Numbers: Practice Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-9: Homework & Practice Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Homework & Practice Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Mixed Numbers: Quick Check Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Reteach to Build Understanding Worksheet Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Enrichment Worksheet 9-9: Center Games Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Add Mixed Numbers: Another Look Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-9: Practice Buddy: Homework & Practice Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Subtract Mixed Numbers Student's Edition eText: Grade 4 Lesson 9-10 Interactive Student Edition: Grade 4 Lesson 9-10 Student's Edition ACTIVe-book: Grade 4 Lesson 9-10 Math Anytime Subtract Mixed Numbers: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Subtract Mixed Numbers: Solve & Share Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Subtract Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Mixed Numbers: Convince Me! Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Mixed Numbers: Practice Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 9-10: Homework & Practice Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Homework & Practice Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Mixed Numbers: Quick Check Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Reteach to Build Understanding Worksheet Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Enrichment Worksheet 9-10: Center Games Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Subtract Mixed Numbers: Another Look Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-10: Practice Buddy: Homework & Practice Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-11: Problem Solving: Model with Math Student's Edition eText: Grade 4 Lesson 9-11 Interactive Student Edition: Grade 4 Lesson 9-11 Student's Edition ACTIVe-book: Grade 4 Lesson 9-11 Math Anytime Problem Solving: Model with Math: Review Topic 9: Today's Challenge Develop: Problem-Based Learning Problem Solving: Model with Math: Solve & Share Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Develop: Visual Learning Problem Solving: Model with Math: Visual Learning Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Problem Solving: Model with Math: Convince Me! Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Problem Solving: Model with Math: Practice Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. 9-11: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Assess & Differentiate 9-11: Homework & Practice Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. 9-11: Homework & Practice Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Problem Solving: Model with Math: Quick Check Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. 9-11: Reteach to Build Understanding Worksheet Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. 9-11: Enrichment Worksheet 9-11: Problem-Solving Reading Activity Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Game: Save the Word: Grade 4 Topics 1–8 Problem Solving: Model with Math: Another Look Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. 9-11: Practice Buddy: Homework & Practice Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. End Topic Interactive Student Edition: End Topic 9 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 9 Assessment Interactive Student Edition: Topic 9 Performance Assessment Problem Solving: Model with Math: Visual Learning Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Model with mathematics. Model with mathematics. Game: Factory Frenzy - Fractions Decompose Fractions: Visual Learning Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Subtraction of Fractions: Visual Learning Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 9-5: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add and Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Estimate Fraction Sums and Differences: Visual Learning Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Model Addition and Subtraction of Mixed Numbers: Visual Learning Curriculum Standards: Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 9 Online Assessment Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Solve problems involving joining parts of the same whole by adding fractions. Use tools such as fraction strips, area models, and number lines to subtract fractions. Solve problems involving separating parts of the same whole by subtracting fractions. Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Use previously-learned concepts and skills to represent and solve problems. Use number lines and benchmark fractions to estimate fraction sums and differences. Count forward or backward on a number line to add or subtract. Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Use models and equivalent fractions to add and subtract mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. Model with mathematics. Model with mathematics. Topic 10: Extend Multiplication Concepts to Fractions Topic 10: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 10 Math and Science Project Review What You Know Vocabulary Cards 10-1: Fractions as Multiples of Unit Fractions: Use Models Student's Edition eText: Grade 4 Lesson 10-1 Interactive Student Edition: Grade 4 Lesson 10-1 Student's Edition ACTIVe-book: Grade 4 Lesson 10-1 Math Anytime Fractions as Multiples of Unit Fractions: Use Models: Review Topic 10: Today's Challenge Develop: Problem-Based Learning Fractions as Multiples of Unit Fractions: Use Models: Solve & Share Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Develop: Visual Learning Fractions as Multiples of Unit Fractions: Use Models: Visual Learning Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Fractions as Multiples of Unit Fractions: Use Models: Convince Me! Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Fractions as Multiples of Unit Fractions: Use Models: Practice Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Assess & Differentiate 10-1: Homework & Practice Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-1: Homework & Practice Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Fractions as Multiples of Unit Fractions: Use Models: Quick Check Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-1: Reteach to Build Understanding Worksheet Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-1: Enrichment Worksheet 10-1: Problem-Solving Reading Activity Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Fractions as Multiples of Unit Fractions: Use Models: Another Look Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-1: Practice Buddy: Homework & Practice Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Multiply a Fraction by a Whole Number: Use Models Student's Edition eText: Grade 4 Lesson 10-2 Interactive Student Edition: Grade 4 Lesson 10-2 Student's Edition ACTIVe-book: Grade 4 Lesson 10-2 Math Anytime Multiply a Fraction by a Whole Number: Use Models: Review Topic 10: Today's Challenge Develop: Problem-Based Learning Multiply a Fraction by a Whole Number: Use Models: Solve & Share Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Develop: Visual Learning Multiply a Fraction by a Whole Number: Use Models: Visual Learning Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Models: Convince Me! Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Models: Practice Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Assess & Differentiate 10-2: Homework & Practice Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Homework & Practice Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Models: Quick Check Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Enrichment Worksheet 10-2: Math and Science Activity Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Multiply a Fraction by a Whole Number: Use Models: Another Look Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Practice Buddy: Homework & Practice Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Multiply a Fraction by a Whole Number: Use Symbols Student's Edition eText: Grade 4 Lesson 10-3 Interactive Student Edition: Grade 4 Lesson 10-3 Student's Edition ACTIVe-book: Grade 4 Lesson 10-3 Math Anytime Multiply a Fraction by a Whole Number: Use Symbols: Review Topic 10: Today's Challenge Develop: Problem-Based Learning Multiply a Fraction by a Whole Number: Use Symbols: Solve & Share Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Develop: Visual Learning Multiply a Fraction by a Whole Number: Use Symbols: Visual Learning Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Symbols: Convince Me! Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Symbols: Practice Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Assess & Differentiate 10-3: Homework & Practice Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Homework & Practice Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Symbols: Quick Check Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Enrichment Worksheet 10-3: Center Games Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Multiply a Fraction by a Whole Number: Use Symbols: Another Look Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-3: Practice Buddy: Homework & Practice Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Multiply a Whole Number and a Mixed Number Student's Edition eText: Grade 4 Lesson 10-4 Interactive Student Edition: Grade 4 Lesson 10-4 Student's Edition ACTIVe-book: Grade 4 Lesson 10-4 Math Anytime Multiply a Whole Number and a Mixed Number: Review Topic 10: Today's Challenge Develop: Problem-Based Learning Multiply a Whole Number and a Mixed Number: Solve & Share Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Develop: Visual Learning Multiply a Whole Number and a Mixed Number: Visual Learning Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Whole Number and a Mixed Number: Convince Me! Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Whole Number and a Mixed Number: Practice Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Assess & Differentiate 10-4: Homework & Practice Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Homework & Practice Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Whole Number and a Mixed Number: Quick Check Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Enrichment Worksheet 10-4: Problem-Solving Reading Activity Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Digital Math Tool Activities Multiply a Whole Number and a Mixed Number: Another Look Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-4: Practice Buddy: Homework & Practice Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-5: Solve Time Problems Student's Edition eText: Grade 4 Lesson 10-5 Interactive Student Edition: Grade 4 Lesson 10-5 Student's Edition ACTIVe-book: Grade 4 Lesson 10-5 Math Anytime Solve Time Problems: Review Topic 10: Today's Challenge Develop: Problem-Based Learning Solve Time Problems: Solve & Share Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Solve Time Problems: Visual Learning Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Time Problems: Convince Me! Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Time Problems: Practice Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 10-5: Homework & Practice Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Homework & Practice Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Time Problems: Quick Check Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Enrichment Worksheet 10-5: Center Games Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Solve Time Problems: Another Look Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Practice Buddy: Homework & Practice Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-6: Problem Solving: Model With Math Interactive Student Edition: Grade 4 Lesson 10-6 End Topic Interactive Student Edition: End Topic 10 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 10 Assessment Interactive Student Edition: Topic 10 Performance Assessment Problem Solving: Model With Math: Visual Learning Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric). Model with mathematics. Model with mathematics. Fractions as Multiples of Unit Fractions: Use Models: Visual Learning Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Models: Visual Learning Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Symbols: Another Look Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Fraction by a Whole Number: Use Symbols: Visual Learning Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Whole Number and a Mixed Number: Visual Learning Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. 10-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 10-5: Center Games Solve Time Problems: Visual Learning Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 10 Online Assessment Curriculum Standards: Use previously-learned concepts and skills to represent and solve problems. Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Use models to multiply fractions by whole numbers. Use symbols and equations to multiply a fraction by a whole number. Use a model to understand a fraction as a multiple of a unit fraction. Use the four operations to solve problems involving time. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric). Model with mathematics. Model with mathematics. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 11: Represent and Interpret Data on Line Plots Topic 11: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 11 Math and Science Project Review What You Know Vocabulary Cards 11-1: Read Line Plots Student's Edition eText: Grade 4 Lesson 11-1 Interactive Student Edition: Grade 4 Lesson 11-1 Student's Edition ACTIVe-book: Grade 4 Lesson 11-1 Math Anytime Read Line Plots: Review Topic 11: Today's Challenge Develop: Problem-Based Learning Read Line Plots: Solve & Share Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Develop: Visual Learning Read Line Plots: Visual Learning Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Read Line Plots: Convince Me! Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Read Line Plots: Practice Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Assess & Differentiate 11-1: Homework & Practice Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-1: Homework & Practice Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Read Line Plots: Quick Check Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-1: Reteach to Build Understanding Worksheet Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-1: Enrichment Worksheet 11-1: Math and Science Activity Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Game: Factory Frenzy - Fractions Read Line Plots: Another Look Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-1: Practice Buddy: Homework & Practice Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Make Line Plots Student's Edition eText: Grade 4 Lesson 11-2 Interactive Student Edition: Grade 4 Lesson 11-2 Student's Edition ACTIVe-book: Grade 4 Lesson 11-2 Math Anytime Make Line Plots: Review Topic 11: Today's Challenge Develop: Problem-Based Learning Make Line Plots: Solve & Share Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Develop: Visual Learning Make Line Plots: Visual Learning Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Make Line Plots: Convince Me! Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Make Line Plots: Practice Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Assess & Differentiate 11-2: Homework & Practice Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Homework & Practice Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Make Line Plots: Quick Check Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Reteach to Build Understanding Worksheet Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Enrichment Worksheet 11-2: Problem-Solving Reading Activity Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Digital Math Tool Activities Make Line Plots: Another Look Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-2: Practice Buddy: Homework & Practice Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Use Line Plots to Solve Problems Student's Edition eText: Grade 4 Lesson 11-3 Interactive Student Edition: Grade 4 Lesson 11-3 Student's Edition ACTIVe-book: Grade 4 Lesson 11-3 Math Anytime Use Line Plots to Solve Problems: Review Topic 11: Today's Challenge Develop: Problem-Based Learning Use Line Plots to Solve Problems: Solve & Share Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Develop: Visual Learning Use Line Plots to Solve Problems: Visual Learning Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Use Line Plots to Solve Problems: Convince Me! Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Use Line Plots to Solve Problems: Practice Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Assess & Differentiate 11-3: Homework & Practice Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Homework & Practice Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Use Line Plots to Solve Problems: Quick Check Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Enrichment Worksheet 11-3: Math and Science Activity Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Digital Math Tool Activities Use Line Plots to Solve Problems: Another Look Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Practice Buddy: Homework & Practice Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-4: Problem Solving: Critique Reasoning Interactive Student Edition: Grade 4 Lesson 11-4 End Topic Interactive Student Edition: End Topic 11 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 11 Assessment Interactive Student Edition: Topic 11 Performance Assessment Make Line Plots: Visual Learning Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 11-3: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Use Line Plots to Solve Problems: Visual Learning Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. 12-1: Center Games Read Line Plots: Visual Learning Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Topic 11 Online Assessment Curriculum Standards: Read and interpret data using line plots. Solve problems involving line plots and fractions. Represent data using line plots and interpret data in line plots to solve problems. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Create a frequency table and/or line plot to display measurement data. Topic 12: Understand and Compare Decimals Topic 12: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 12 Math and Science Project Review What You Know Vocabulary Cards 12-1: Fractions and Decimals Student's Edition eText: Grade 4 Lesson 12-1 Interactive Student Edition: Grade 4 Lesson 12-1 Student's Edition ACTIVe-book: Grade 4 Lesson 12-1 Math Anytime Fractions and Decimals: Review Topic 12: Today's Challenge Develop: Problem-Based Learning Fractions and Decimals: Solve & Share Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Develop: Visual Learning Fractions and Decimals: Visual Learning Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals: Convince Me! Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals: Practice Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Assess & Differentiate 12-1: Homework & Practice Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-1: Homework & Practice Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals: Quick Check Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-1: Reteach to Build Understanding Worksheet Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-1: Enrichment Worksheet 12-1: Center Games Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Digital Math Tool Activities Fractions and Decimals: Another Look Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-1: Practice Buddy: Homework & Practice Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Fractions and Decimals on the Number Line Student's Edition eText: Grade 4 Lesson 12-2 Interactive Student Edition: Grade 4 Lesson 12-2 Student's Edition ACTIVe-book: Grade 4 Lesson 12-2 Math Anytime Fractions and Decimals on the Number Line: Review Topic 12: Today's Challenge Develop: Problem-Based Learning Fractions and Decimals on the Number Line: Solve & Share Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Develop: Visual Learning Fractions and Decimals on the Number Line: Visual Learning Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals on the Number Line: Convince Me! Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals on the Number Line: Practice Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Assess & Differentiate 12-2: Homework & Practice Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Homework & Practice Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals on the Number Line: Quick Check Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Reteach to Build Understanding Worksheet Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Enrichment Worksheet 12-2: Problem-Solving Reading Activity Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Digital Math Tool Activities Fractions and Decimals on the Number Line: Another Look Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-2: Practice Buddy: Homework & Practice Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 12-3: Compare Decimals Student's Edition eText: Grade 4 Lesson 12-3 Interactive Student Edition: Grade 4 Lesson 12-3 Student's Edition ACTIVe-book: Grade 4 Lesson 12-3 Math Anytime Compare Decimals: Review Topic 12: Today's Challenge Develop: Problem-Based Learning Compare Decimals: Solve & Share Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Develop: Visual Learning Compare Decimals: Visual Learning Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Compare Decimals: Convince Me! Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Compare Decimals: Practice Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Assess & Differentiate 12-3: Homework & Practice Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-3: Homework & Practice Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Compare Decimals: Quick Check Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-3: Reteach to Build Understanding Worksheet Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-3: Enrichment Worksheet 12-3: Center Games Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Digital Math Tool Activities Compare Decimals: Another Look Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-3: Practice Buddy: Homework & Practice Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. 12-4: Add Fractions with Denominators of 10 and 100 Student's Edition eText: Grade 4 Lesson 12-4 Interactive Student Edition: Grade 4 Lesson 12-4 Student's Edition ACTIVe-book: Grade 4 Lesson 12-4 Math Anytime Add Fractions with Denominators of 10 and 100: Review Topic 12: Today's Challenge Develop: Problem-Based Learning Add Fractions with Denominators of 10 and 100: Solve & Share Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Develop: Visual Learning Add Fractions with Denominators of 10 and 100: Visual Learning Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Denominators of 10 and 100: Convince Me! Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Denominators of 10 and 100: Practice Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Assess & Differentiate 12-4: Homework & Practice Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-4: Homework & Practice Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Fractions with Denominators of 10 and 100: Quick Check Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-4: Reteach to Build Understanding Worksheet Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-4: Enrichment Worksheet 12-4: Problem-Solving Reading Activity Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Digital Math Tool Activities Add Fractions with Denominators of 10 and 100: Another Look Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-4: Practice Buddy: Homework & Practice Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. 12-5: Solve Word Problems Involving Money Student's Edition eText: Grade 4 Lesson 12-5 Interactive Student Edition: Grade 4 Lesson 12-5 Student's Edition ACTIVe-book: Grade 4 Lesson 12-5 Math Anytime Solve Word Problems Involving Money: Review Topic 12: Today's Challenge Develop: Problem-Based Learning Solve Word Problems Involving Money: Solve & Share Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Solve Word Problems Involving Money: Visual Learning Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Word Problems Involving Money: Convince Me! Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Word Problems Involving Money: Practice Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 12-5: Homework & Practice Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-5: Homework & Practice Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Word Problems Involving Money: Quick Check Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-5: Enrichment Worksheet 12-5: Math and Science Activity Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Solve Word Problems Involving Money: Another Look Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-5: Practice Buddy: Homework & Practice Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 12-6: Problem Solving: Look For & Use Structure Student's Edition eText: Grade 4 Lesson 12-6 Interactive Student Edition: Grade 4 Lesson 12-6 Student's Edition ACTIVe-book: Grade 4 Lesson 12-6 Math Anytime Problem Solving: Look For & Use Structure: Review Topic 12: Today's Challenge Develop: Problem-Based Learning Problem Solving: Look For & Use Structure: Solve & Share Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Develop: Visual Learning Problem Solving: Look For & Use Structure: Visual Learning Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Problem Solving: Look For & Use Structure: Convince Me! Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Problem Solving: Look For & Use Structure: Practice Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. 12-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Assess & Differentiate 12-6: Homework & Practice Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. 12-6: Homework & Practice Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Problem Solving: Look For & Use Structure: Quick Check Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. 12-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. 12-6: Enrichment Worksheet 12-6: Math and Science Activity Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. Game: Save the Word: Grade 4 Topics 1–12 Problem Solving: Look For & Use Structure: Another Look Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. 12-6: Practice Buddy: Homework & Practice Curriculum Standards: Use the structure of the place-value system for decimals to solve problems. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real- world and mathematical situations. Look for and make use of structure. Look for and make use of structure. End Topic Interactive Student Edition: End Topic 12 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 12 Assessment Interactive Student Edition: Topic 12 Performance Assessment Game: Factory Frenzy - Decimals Solve Word Problems Involving Money: Visual Learning Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Fractions and Decimals: Visual Learning Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Fractions and Decimals on the Number Line: Visual Learning Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Compare Decimals: Visual Learning Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Add Fractions with Denominators of 10 and 100: Visual Learning Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Topic 12 Online Assessment Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Locate and describe fractions and decimals on number lines. Relate fractions and decimals with denominators of 10 to 100. Compare decimals by reasoning about their size. Use fractions or decimals to solve word problems involving money. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. The student will read, write, represent, and identify decimals expressed through thousandths. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1 Center Games H16: Equivalent Fractions Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. I39: More Elapsed Time Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. J11: Draw a Strip Diagram and Write an Equation Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. H10: Comparing Fractions on the Number Line Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. I40: Elapsed Time in Other Units Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I60: Making Line Plots Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. I61: Interpreting Graphs Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. H18: Estimating Fractional Amounts Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. H25: Decimals on the Number Line Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. H30: Comparing and Ordering Decimals Through Hundredths Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. H31: Comparing and Ordering Decimals Through Thousandths Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. H38: Adding Fractions with Like Denominators Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H39: Subtracting Fractions with Like Denominators Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H40: Adding and Subtracting Fractions with Like Denominators Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H41: Adding and Subtracting Fractions on a Number Line Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H42: Adding Fractions with Unlike Denominators Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. H46: Subtracting Mixed Numbers Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H47: Multiplying Fractions by Whole Numbers Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. H52: Multiplying Mixed Numbers Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. J5: Multi-Step Problems Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Equivalent Fractions: Area Models: Visual Learning Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Generate Equivalent Fractions: Division: Visual Learning Curriculum Standards: Use division to find equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Recognize and generate equivalent fractions. Use Benchmarks to Compare Fractions: Visual Learning Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Compare Fractions: Visual Learning Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Add Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add and Subtract Fractions with Like Denominators: Visual Learning Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Estimate Fraction Sums and Differences: Visual Learning Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Mental Math: Estimate Quotients for Greater Dividends: Visual Learning Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Interpret Remainders: Visual Learning Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve Comparison Situations: Visual Learning Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Factors: Visual Learning Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one- digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Prime and Composite Numbers: Visual Learning Curriculum Standards: Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Subtract Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Multiply a Fraction by a Whole Number: Use Symbols: Visual Learning Curriculum Standards: Use symbols and equations to multiply a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Multiply a Whole Number and a Mixed Number: Visual Learning Curriculum Standards: Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Solve Time Problems: Visual Learning Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Read Line Plots: Visual Learning Curriculum Standards: Read and interpret data using line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Make Line Plots: Visual Learning Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Use Line Plots to Solve Problems: Visual Learning Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Fractions and Decimals on the Number Line: Visual Learning Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Compare Decimals: Visual Learning Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Add Fractions with Denominators of 10 and 100: Visual Learning Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve Word Problems Involving Money: Visual Learning Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. G57: Factoring Numbers Curriculum Standards: Use multiplication to find all the factor pairs for a whole number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one- digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. G12: Adding and Subtracting Money Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. G51: Interpret the Remainder Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. G75: Dividing Greater Numbers Curriculum Standards: Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3- digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. H8: Using Models to Compare Fractions Curriculum Standards: Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. H9: Using Models to Find Equivalent Fractions Curriculum Standards: Use area models to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Topics 1–12: Online Cumulative/Benchmark Assessment Curriculum Standards: Use appropriate tools strategically. Model with mathematics. Look for and make use of structure. Attend to precision. Add fractions with denominators of 10 and 100 by using equivalent fractions. Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Locate and describe fractions and decimals on number lines. Use models or rename fractions to compare. Read and interpret data using line plots. Make sense of problems and persevere in solving them. Represent data using line plots and interpret data in line plots to solve problems. Construct viable arguments and critique the reasoning of others. Reason abstractly and quantitatively. Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. Compare decimals by reasoning about their size. Use fractions or decimals to solve word problems involving money. Interpret comparisons as multiplication or addition equations. Solve problems involving line plots and fractions. Use benchmarks, area models, and number lines to compare fractions. Use division to find equivalent fractions. Use factors to determine whether a whole number greater than 1 is prime or composite. Solve problems involving joining parts of the same whole by adding fractions. Solve problems involving separating parts of the same whole by subtracting fractions. Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Use symbols and equations to multiply a fraction by a whole number. Solve division problems and interpret remainders. Use multiplication to find all the factor pairs for a whole number. Use area models to recognize and generate equivalent fractions. Use the four operations to solve problems involving time. Use number lines and benchmark fractions to estimate fraction sums and differences. Count forward or backward on a number line to add or subtract. Use appropriate tools strategically. Use appropriate tools strategically. Model with mathematics. Model with mathematics. Look for and make use of structure. Look for and make use of structure. Attend to precision. Attend to precision. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Compare two fractions using the symbols >, = or <, and justify the solution. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Create a frequency table and/or line plot to display measurement data. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one- digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Find whole- number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Interpret remainders in word problems. Explain and/or illustrate why two fractions are equivalent. Solve problems involving the conversion of one measure of time to another. Solve word problems involving addition and subtraction of time intervals that cross the hour. Topic 13: Measurement: Find Equivalence in Units of Measure Topic 13: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 13 Math and Science Project Review What You Know Vocabulary Cards 13-1: Equivalence with Customary Units of Length Student's Edition eText: Grade 4 Lesson 13-1 Interactive Student Edition: Grade 4 Lesson 13-1 Student's Edition ACTIVe-book: Grade 4 Lesson 13-1 Math Anytime Equivalence with Customary Units of Length: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Equivalence with Customary Units of Length: Solve & Share Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Equivalence with Customary Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Length: Convince Me! Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Length: Practice Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 13-1: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Length: Quick Check Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1: Enrichment Worksheet 13-1 Center Games Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Customary Units of Length: Another Look Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-1: Practice Buddy: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Equivalence with Customary Units of Capacity Student's Edition eText: Grade 4 Lesson 13-2 Interactive Student Edition: Grade 4 Lesson 13-2 Student's Edition ACTIVe-book: Grade 4 Lesson 13-2 Math Anytime Equivalence with Customary Units of Capacity: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Equivalence with Customary Units of Capacity: Solve & Share Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Equivalence with Customary Units of Capacity: Visual Learning Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Capacity: Convince Me! Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Capacity: Practice Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 13-2: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Capacity: Quick Check Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Enrichment Worksheet 13-2 Math and Science Activity Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Customary Units of Capacity: Another Look Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Practice Buddy: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Equivalence with Customary Units of Weight Student's Edition eText: Grade 4 Lesson 13-3 Interactive Student Edition: Grade 4 Lesson 13-3 Student's Edition ACTIVe-book: Grade 4 Lesson 13-3 Math Anytime Equivalence with Customary Units of Weight: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Equivalence with Customary Units of Weight: Solve & Share Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Equivalence with Customary Units of Weight: Visual Learning Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Weight: Convince Me! Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Units of Weight: Practice Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 13-3: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Weight: Quick Check Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Enrichment Worksheet 13-3 Problem-Solving Reading Activity Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Customary Units of Weight: Another Look Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-3: Practice Buddy: Homework & Practice Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Equivalence with Metric Units of Length Student's Edition eText: Grade 4 Lesson 13-4 Interactive Student Edition: Grade 4 Lesson 13-4 Student's Edition ACTIVe-book: Grade 4 Lesson 13-4 Math Anytime Equivalence with Metric Units of Length: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Equivalence with Metric Units of Length: Solve & Share Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Equivalence with Metric Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Length: Convince Me! Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Length: Practice Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 13-4: Homework & Practice Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Homework & Practice Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Length: Quick Check Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Enrichment Worksheet 13-4 Center Games Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Game: Galaxy Hunt - Make a Million Equivalence with Metric Units of Length: Another Look Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Practice Buddy: Homework & Practice Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Equivalence with Metric Units of Capacity and Mass Student's Edition eText: Grade 4 Lesson 13-5 Interactive Student Edition: Grade 4 Lesson 13-5 Student's Edition ACTIVe-book: Grade 4 Lesson 13-5 Math Anytime Equivalence with Metric Units of Capacity and Mass: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Equivalence with Metric Units of Capacity and Mass: Solve & Share Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Develop: Visual Learning Equivalence with Metric Units of Capacity and Mass: Visual Learning Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Capacity and Mass: Convince Me! Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Capacity and Mass: Practice Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Assess & Differentiate 13-5: Homework & Practice Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Homework & Practice Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Capacity and Mass: Quick Check Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Enrichment Worksheet 13-5 Math and Science Activity Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Digital Math Tool Activities Equivalence with Metric Units of Capacity and Mass: Another Look Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-5: Practice Buddy: Homework & Practice Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-6: Solve Perimeter and Area Problems Student's Edition eText: Grade 4 Lesson 13-6 Interactive Student Edition: Grade 4 Lesson 13-6 Student's Edition ACTIVe-book: Grade 4 Lesson 13-6 Math Anytime Solve Perimeter and Area Problems: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Solve Perimeter and Area Problems: Solve & Share Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Develop: Visual Learning Solve Perimeter and Area Problems: Visual Learning Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Solve Perimeter and Area Problems: Convince Me! Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Solve Perimeter and Area Problems: Practice Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Assess & Differentiate 13-6: Homework & Practice Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-6: Homework & Practice Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Solve Perimeter and Area Problems: Quick Check Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-6: Reteach to Build Understanding Worksheet Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-6: Enrichment Worksheet 13-6 Center Games Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Digital Math Tool Activities Solve Perimeter and Area Problems: Another Look Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-6: Practice Buddy: Homework & Practice Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 13-7: Problem Solving: Precision Student's Edition eText: Grade 4 Lesson 13-7 Interactive Student Edition: Grade 4 Lesson 13-7 Student's Edition ACTIVe-book: Grade 4 Lesson 13-7 Math Anytime Problem Solving: Precision: Review Topic 13: Today's Challenge Develop: Problem-Based Learning Problem Solving: Precision: Solve & Share Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Develop: Visual Learning Problem Solving: Precision: Visual Learning Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Problem Solving: Precision: Convince Me! Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Problem Solving: Precision: Practice Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. 13-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Assess & Differentiate 13-7: Homework & Practice Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. 13-7: Homework & Practice Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Problem Solving: Precision: Quick Check Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. 13-7: Reteach to Build Understanding Worksheet Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. 13-7: Enrichment Worksheet 13-7 Problem-Solving Reading Activity Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. Game: Save the Word: Grade 4 Topics 1–12 Problem Solving: Precision: Another Look Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. 13-7: Practice Buddy: Homework & Practice Curriculum Standards: Be precise when solving measurement problems. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will estimate and determine sums, differences, and products of whole numbers. The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Attend to precision. Attend to precision. End Topic Interactive Student Edition: End Topic 13 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 13 Assessment Interactive Student Edition: Topic 13 Performance Assessment Solve Perimeter and Area Problems: Visual Learning Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. 15-2: Center Games Equivalence with Customary Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-2: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Capacity: Visual Learning Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Weight: Visual Learning Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. 13-4: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Capacity and Mass: Another Look Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Capacity and Mass: Visual Learning Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Topic 13 Online Assessment Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Find the unknown length or width of a rectangle using the known area or perimeter. Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Topic 14: Algebra: Generate and Analyze Patterns Topic 14: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 14 Math and Science Project Review What You Know Vocabulary Cards 14-1: Number Sequences Student's Edition eText: Grade 4 Lesson 14-1 Interactive Student Edition: Grade 4 Lesson 14-1 Student's Edition ACTIVe-book: Grade 4 Lesson 14-1 Math Anytime Number Sequences: Review Topic 14: Today's Challenge Develop: Problem-Based Learning Number Sequences: Solve & Share Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Develop: Visual Learning Number Sequences: Visual Learning Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Number Sequences: Convince Me! Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Number Sequences: Practice Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Assess & Differentiate 14-1: Homework & Practice Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-1: Homework & Practice Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Number Sequences: Quick Check Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-1: Reteach to Build Understanding Worksheet Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-1: Enrichment Worksheet 14-1 Problem-Solving Reading Activity Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Game: Fluency - Add and Subtract Multi-Digit Whole Numbers Number Sequences: Another Look Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-1: Practice Buddy: Homework & Practice Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Patterns: Number Rules Student's Edition eText: Grade 4 Lesson 14-2 Interactive Student Edition: Grade 4 Lesson 14-2 Student's Edition ACTIVe-book: Grade 4 Lesson 14-2 Math Anytime Patterns: Number Rules: Review Topic 14: Today's Challenge Develop: Problem-Based Learning Patterns: Number Rules: Solve & Share Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Develop: Visual Learning Patterns: Number Rules: Visual Learning Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Number Rules: Convince Me! Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Number Rules: Practice Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Assess & Differentiate 14-2: Homework & Practice Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Homework & Practice Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Number Rules: Quick Check Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Reteach to Build Understanding Worksheet Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Enrichment Worksheet 14-2 Problem-Solving Reading Activity Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Digital Math Tool Activities Patterns: Number Rules: Another Look Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-2: Practice Buddy: Homework & Practice Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Patterns: Repeating Shapes Student's Edition eText: Grade 4 Lesson 14-3 Interactive Student Edition: Grade 4 Lesson 14-3 Student's Edition ACTIVe-book: Grade 4 Lesson 14-3 Math Anytime Patterns: Repeating Shapes: Review Topic 14: Today's Challenge Develop: Problem-Based Learning Patterns: Repeating Shapes: Solve & Share Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Develop: Visual Learning Patterns: Repeating Shapes: Visual Learning Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Repeating Shapes: Convince Me! Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Repeating Shapes: Practice Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Assess & Differentiate 14-3: Homework & Practice Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Homework & Practice Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Repeating Shapes: Quick Check Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Reteach to Build Understanding Worksheet Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Enrichment Worksheet 14-3 Math and Science Activity Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Digital Math Tool Activities Patterns: Repeating Shapes: Another Look Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-3: Practice Buddy: Homework & Practice Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. 14-4: Problem Solving: Look For & Use Structure Student's Edition eText: Grade 4 Lesson 14-4 Interactive Student Edition: Grade 4 Lesson 14-4 Student's Edition ACTIVe-book: Grade 4 Lesson 14-4 Math Anytime Problem Solving: Look For & Use Structure: Review Topic 14: Today's Challenge Develop: Problem-Based Learning Problem Solving: Look For & Use Structure: Solve & Share Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Develop: Visual Learning Problem Solving: Look For & Use Structure: Visual Learning Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Problem Solving: Look For & Use Structure: Convince Me! Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Problem Solving: Look For & Use Structure: Practice Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. 14-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Assess & Differentiate 14-4: Homework & Practice Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. 14-4: Homework & Practice Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Problem Solving: Look For & Use Structure: Quick Check Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. 14-4: Reteach to Build Understanding Worksheet Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. 14-4: Enrichment Worksheet 14-4 Math and Science Activity Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Digital Math Tool Activities Problem Solving: Look For & Use Structure: Another Look Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. 14-4: Practice Buddy: Homework & Practice Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. End Topic Interactive Student Edition: End Topic 14 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 14 Assessment Interactive Student Edition: Topic 14 Performance Assessment 16-2: Center Games Number Sequences: Visual Learning Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Number Rules: Visual Learning Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Patterns: Repeating Shapes: Visual Learning Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Topic 14 Online Assessment Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a shape pattern that follows a given rule and predict a shape in the pattern. Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Topic 15: Understand Concepts of Angle and Angle Measurement Topic 15: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 15 Math and Science Project Review What You Know Vocabulary Cards 15-1: Lines, Rays, and Angles Student's Edition eText: Grade 4 Lesson 15-1 Interactive Student Edition: Grade 4 Lesson 15-1 Student's Edition ACTIVe-book: Grade 4 Lesson 15-1 Math Anytime Lines, Rays, and Angles: Review Topic 15: Today's Challenge Develop: Problem-Based Learning Lines, Rays, and Angles: Solve & Share Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Develop: Visual Learning Lines, Rays, and Angles: Visual Learning Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Lines, Rays, and Angles: Convince Me! Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Lines, Rays, and Angles: Practice Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Assess & Differentiate 15-1: Homework & Practice Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Homework & Practice Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Lines, Rays, and Angles: Quick Check Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Enrichment Worksheet 15-1: Center Games Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Digital Math Tool Activities Lines, Rays, and Angles: Another Look Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Practice Buddy: Homework & Practice Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-2: Understand Angles and Unit Angles Student's Edition eText: Grade 4 Lesson 15-2 Interactive Student Edition: Grade 4 Lesson 15-2 Student's Edition ACTIVe-book: Grade 4 Lesson 15-2 Math Anytime Understand Angles and Unit Angles: Review Topic 15: Today's Challenge Develop: Problem-Based Learning Understand Angles and Unit Angles: Solve & Share Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Develop: Visual Learning Understand Angles and Unit Angles: Visual Learning Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Understand Angles and Unit Angles: Convince Me! Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Understand Angles and Unit Angles: Practice Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Assess & Differentiate 15-2: Homework & Practice Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-2: Homework & Practice Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Understand Angles and Unit Angles: Quick Check Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-2: Reteach to Build Understanding Worksheet Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-2: Enrichment Worksheet 15-2: Center Games Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Digital Math Tool Activities Understand Angles and Unit Angles: Another Look Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-2: Practice Buddy: Homework & Practice Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. 15-3: Measure with Unit Angles Student's Edition eText: Grade 4 Lesson 15-3 Interactive Student Edition: Grade 4 Lesson 15-3 Student's Edition ACTIVe-book: Grade 4 Lesson 15-3 Math Anytime Measure with Unit Angles: Review Topic 15: Today's Challenge Develop: Problem-Based Learning Measure with Unit Angles: Solve & Share Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Develop: Visual Learning Measure with Unit Angles: Visual Learning Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Measure with Unit Angles: Convince Me! Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Measure with Unit Angles: Practice Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Assess & Differentiate 15-3: Homework & Practice Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Homework & Practice Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Measure with Unit Angles: Quick Check Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Enrichment Worksheet 15-3: Problem-Solving Reading Activity Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Digital Math Tool Activities Measure with Unit Angles: Another Look Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Practice Buddy: Homework & Practice Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-4: Measure and Draw Angles Student's Edition eText: Grade 4 Lesson 15-4 Interactive Student Edition: Grade 4 Lesson 15-4 Student's Edition ACTIVe-book: Grade 4 Lesson 15-4 Math Anytime Measure and Draw Angles: Review Topic 15: Today's Challenge Develop: Problem-Based Learning Measure and Draw Angles: Solve & Share Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Develop: Visual Learning Measure and Draw Angles: Visual Learning Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Measure and Draw Angles: Convince Me! Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Measure and Draw Angles: Practice Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Assess & Differentiate 15-4: Homework & Practice Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-4: Homework & Practice Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Measure and Draw Angles: Quick Check Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-4: Reteach to Build Understanding Worksheet Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-4: Enrichment Worksheet 15-4: Math and Science Activity Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Game: Save the Word: Grade 4 Topics 1–12 Measure and Draw Angles: Another Look Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-4: Practice Buddy: Homework & Practice Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. 15-5: Add and Subtract Angle Measures Student's Edition eText: Grade 4 Lesson 15-5 Interactive Student Edition: Grade 4 Lesson 15-5 Student's Edition ACTIVe-book: Grade 4 Lesson 15-5 Math Anytime Add and Subtract Angle Measures: Review Topic 15: Today's Challenge Develop: Problem-Based Learning Add and Subtract Angle Measures: Solve & Share Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Develop: Visual Learning Add and Subtract Angle Measures: Visual Learning Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Add and Subtract Angle Measures: Convince Me! Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Add and Subtract Angle Measures: Practice Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Assess & Differentiate 15-5: Homework & Practice Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-5: Homework & Practice Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Add and Subtract Angle Measures: Quick Check Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-5: Reteach to Build Understanding Worksheet Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-5: Enrichment Worksheet 15-5: Math and Science Activity Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Digital Math Tool Activities Add and Subtract Angle Measures: Another Look Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-5: Practice Buddy: Homework & Practice Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 15-6: Problem Solving: Use Appropriate Tools Student's Edition eText: Grade 4 Lesson 15-6 Interactive Student Edition: Grade 4 Lesson 15-6 Student's Edition ACTIVe-book: Grade 4 Lesson 15-6 Math Anytime Problem Solving: Use Appropriate Tools: Review Topic 15: Today's Challenge Develop: Problem-Based Learning Problem Solving: Use Appropriate Tools: Solve & Share Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Develop: Visual Learning Problem Solving: Use Appropriate Tools: Visual Learning Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Problem Solving: Use Appropriate Tools: Convince Me! Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Problem Solving: Use Appropriate Tools: Practice Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. 15-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Assess & Differentiate 15-6: Homework & Practice Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. 15-6: Homework & Practice Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Problem Solving: Use Appropriate Tools: Quick Check Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. 15-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. 15-6: Enrichment Worksheet 15-6: Problem-Solving Reading Activity Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. Digital Math Tool Activities Problem Solving: Use Appropriate Tools: Another Look Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. 15-6: Practice Buddy: Homework & Practice Curriculum Standards: Use appropriate tools, such as a protractor and ruler, to solve problems. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Use appropriate tools strategically. Use appropriate tools strategically. End Topic Interactive Student Edition: End Topic 15 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 15 Assessment Interactive Student Edition: Topic 15 Performance Assessment Understand Angles and Unit Angles: Visual Learning Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Measure with Unit Angles: Visual Learning Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-3: Reteach to Build Understanding Worksheet Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Measure and Draw Angles: Visual Learning Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole- number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Add and Subtract Angle Measures: Visual Learning Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. 16-1: Center Games Lines, Rays, and Angles: Visual Learning Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. 15-1: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Topic 15 Online Assessment Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Find the measure of an angle that turns through a fraction of a circle. Use known angle measures to measure unknown angles. Use addition and subtraction to solve problems with unknown angle measures. Use a protractor to measure and draw angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in whole- number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Measure and sketch angles in whole- number degrees using a protractor. Draw and measure angles in whole-number degrees using a protractor. Topic 16: Lines, Angles, and Shapes Topic 16: Today's Challenge Begin Topic Interactive Student Edition: Begin Topic 16 Math and Science Project Review What You Know Vocabulary Cards 16-1: Lines Student's Edition eText: Grade 4 Lesson 16-1 Interactive Student Edition: Grade 4 Lesson 16-1 Student's Edition ACTIVe-book: Grade 4 Lesson 16-1 Math Anytime Lines: Review Topic 16: Today's Challenge Develop: Problem-Based Learning Lines: Solve & Share Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Develop: Visual Learning Lines: Visual Learning Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Lines: Convince Me! Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Lines: Practice Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Assess & Differentiate 16-1: Homework & Practice Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-1: Homework & Practice Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Lines: Quick Check Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-1: Reteach to Build Understanding Worksheet Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-1: Enrichment Worksheet 16-1: Center Games Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Digital Math Tool Activities Lines: Another Look Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-1: Practice Buddy: Homework & Practice Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. 16-2: Classify Triangles Student's Edition eText: Grade 4 Lesson 16-2 Interactive Student Edition: Grade 4 Lesson 16-2 Student's Edition ACTIVe-book: Grade 4 Lesson 16-2 Math Anytime Classify Triangles: Review Topic 16: Today's Challenge Develop: Problem-Based Learning Classify Triangles: Solve & Share Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Develop: Visual Learning Classify Triangles: Visual Learning Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Classify Triangles: Convince Me! Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Classify Triangles: Practice Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Assess & Differentiate 16-2: Homework & Practice Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-2: Homework & Practice Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Classify Triangles: Quick Check Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-2: Reteach to Build Understanding Worksheet Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-2: Enrichment Worksheet 16-2: Center Games Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Digital Math Tool Activities Classify Triangles: Another Look Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-2: Practice Buddy: Homework & Practice Curriculum Standards: Classify triangles by line segments and angles. Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. 16-3: Classify Quadrilaterals Student's Edition eText: Grade 4 Lesson 16-3 Interactive Student Edition: Grade 4 Lesson 16-3 Student's Edition ACTIVe-book: Grade 4 Lesson 16-3 Math Anytime Classify Quadrilaterals: Review Topic 16: Today's Challenge Develop: Problem-Based Learning Classify Quadrilaterals: Solve & Share Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Develop: Visual Learning Classify Quadrilaterals: Visual Learning Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Classify Quadrilaterals: Convince Me! Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Classify Quadrilaterals: Practice Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Assess & Differentiate 16-3: Homework & Practice Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-3: Homework & Practice Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Classify Quadrilaterals: Quick Check Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-3: Reteach to Build Understanding Worksheet Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-3: Enrichment Worksheet 16-3: Problem-Solving Reading Activity Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Digital Math Tool Activities Classify Quadrilaterals: Another Look Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-3: Practice Buddy: Homework & Practice Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. 16-4: Line Symmetry Student's Edition eText: Grade 4 Lesson 16-4 Interactive Student Edition: Grade 4 Lesson 16-4 Student's Edition ACTIVe-book: Grade 4 Lesson 16-4 Math Anytime Line Symmetry: Review Topic 16: Today's Challenge Develop: Problem-Based Learning Line Symmetry: Solve & Share Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Develop: Visual Learning Line Symmetry: Visual Learning Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Line Symmetry: Convince Me! Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Line Symmetry: Practice Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Assess & Differentiate 16-4: Homework & Practice Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-4: Homework & Practice Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Line Symmetry: Quick Check Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-4: Reteach to Build Understanding Worksheet Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-4: Enrichment Worksheet 16-4: Math and Science Activity Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Digital Math Tool Activities Line Symmetry: Another Look Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-4: Practice Buddy: Homework & Practice Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Draw Shapes with Line Symmetry Student's Edition eText: Grade 4 Lesson 16-5 Interactive Student Edition: Grade 4 Lesson 16-5 Student's Edition ACTIVe-book: Grade 4 Lesson 16-5 Math Anytime Draw Shapes with Line Symmetry: Review Topic 16: Today's Challenge Develop: Problem-Based Learning Draw Shapes with Line Symmetry: Solve & Share Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Develop: Visual Learning Draw Shapes with Line Symmetry: Visual Learning Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Draw Shapes with Line Symmetry: Convince Me! Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Draw Shapes with Line Symmetry: Practice Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Assess & Differentiate 16-5: Homework & Practice Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Homework & Practice Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Draw Shapes with Line Symmetry: Quick Check Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Reteach to Build Understanding Worksheet Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Enrichment Worksheet 16-5: Math and Science Activity Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Game: Save the Word: Grade 4 Topics 1–16 Draw Shapes with Line Symmetry: Another Look Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-5: Practice Buddy: Homework & Practice Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. 16-6: Problem Solving: Critique Reasoning Student's Edition eText: Grade 4 Lesson 16-6 Interactive Student Edition: Grade 4 Lesson 16-6 Student's Edition ACTIVe-book: Grade 4 Lesson 16-6 Math Anytime Problem Solving: Critique Reasoning: Review Topic 16: Today's Challenge Develop: Problem-Based Learning Problem Solving: Critique Reasoning: Solve & Share Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Develop: Visual Learning Problem Solving: Critique Reasoning: Visual Learning Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Critique Reasoning: Convince Me! Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Critique Reasoning: Practice Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 16-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Assess & Differentiate 16-6: Homework & Practice Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 16-6: Homework & Practice Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Problem Solving: Critique Reasoning: Quick Check Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 16-6: Reteach to Build Understanding Worksheet Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 16-6: Enrichment Worksheet 16-6: Problem-Solving Reading Activity Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Game: Save the Word: Grade 4 Topics 1–16 Problem Solving: Critique Reasoning: Another Look Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. 16-6: Practice Buddy: Homework & Practice Curriculum Standards: Use understanding of two-dimensional shapes to critique the reasoning of others. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. End Topic Interactive Student Edition: End Topic 16 Fluency Practice Activity Vocabulary Review Reteaching Interactive Student Edition: Topic 15 Assessment Interactive Student Edition: Topic 15 Performance Assessment 13-6 Center Games Lines: Visual Learning Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Classify Triangles: Visual Learning Curriculum Standards: Classify triangles by line segments and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Classify Quadrilaterals: Visual Learning Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Line Symmetry: Visual Learning Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Draw Shapes with Line Symmetry: Visual Learning Curriculum Standards: Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Topic 16 Online Assessment Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Recognize and draw lines of symmetry. Identify line symmetric figures. Draw figures that have line symmetry. Classify triangles by line segments and angles. Classify quadrilaterals by lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. H38: Adding Fractions with Like Denominators Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Line Symmetry: Visual Learning Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. I2: Lines and Line Segments Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. I10: Line Symmetry Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. H30: Comparing and Ordering Decimals Through Hundredths Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. H15: Using Money to Understand Decimals Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. H25: Decimals on the Number Line Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. 15-1: Center Games Decompose Fractions: Visual Learning Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Model Subtraction of Fractions: Visual Learning Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Add Mixed Numbers: Visual Learning Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Multiply a Fraction by a Whole Number: Use Models: Visual Learning Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Use Line Plots to Solve Problems: Visual Learning Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Compare Decimals: Visual Learning Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. Solve Word Problems Involving Money: Visual Learning Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Length: Visual Learning Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Capacity: Visual Learning Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Customary Units of Weight: Visual Learning Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Equivalence with Metric Units of Capacity and Mass: Visual Learning Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve Perimeter and Area Problems: Visual Learning Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Patterns: Number Rules: Visual Learning Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Problem Solving: Look For & Use Structure: Visual Learning Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Lines, Rays, and Angles: Visual Learning Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Understand Angles and Unit Angles: Visual Learning Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Measure with Unit Angles: Visual Learning Curriculum Standards: Use known angle measures to measure unknown angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Measure and Draw Angles: Visual Learning Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole- number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. Add and Subtract Angle Measures: Visual Learning Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Lines: Visual Learning Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Classify Triangles: Visual Learning Curriculum Standards: Classify triangles by line segments and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Classify Quadrilaterals: Visual Learning Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. H45: Adding Mixed Numbers Curriculum Standards: Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H40: Adding and Subtracting Fractions with Like Denominators Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H47: Multiplying Fractions by Whole Numbers Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. H52: Multiplying Mixed Numbers Curriculum Standards: Use models to multiply fractions by whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. I18: Measuring and Classifying Angles Curriculum Standards: Use a protractor to measure and draw angles. Measure angles in whole- number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Measure and sketch angles in whole-number degrees using a protractor. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. I19: Angle Pairs Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. I27: Using Metric Units of Mass Curriculum Standards: Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I30: Units of Time Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I32: Converting Customary Units of Length Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I33: Converting Customary Units of Capacity Curriculum Standards: Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I34: Converting Customary Units of Weight Curriculum Standards: Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I45: Area of Rectangles and Squares Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. I47: Rectangles with the Same Area or Perimeter Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. I71: Line Plots Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. F27: Geometric Growth Patterns Curriculum Standards: Solve problems by using patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. I3: Acute, Right, and Obtuse Angles Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. I5: Classifying Triangles Using Sides and Angles Curriculum Standards: Classify triangles by line segments and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. I6: Quadrilaterals Curriculum Standards: Classify quadrilaterals by lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Topics 1–16: Online Cumulative/Benchmark Assessment Curriculum Standards: Use appropriate tools strategically. Model with mathematics. Attend to precision. Look for and express regularity in repeated reasoning. Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Find the measure of an angle that turns through a fraction of a circle. Draw and identify perpendicular, parallel, and intersecting lines. Locate and describe fractions and decimals on number lines. Find the unknown length or width of a rectangle using the known area or perimeter. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Reason abstractly and quantitatively. Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Use addition and subtraction to solve problems with unknown angle measures. Recognize and draw lines of symmetry. Identify line symmetric figures. Use models to multiply fractions by whole numbers. Solve problems by using patterns. Classify triangles by line segments and angles. Use a protractor to measure and draw angles. Classify quadrilaterals by lines and angles. Recognize and draw lines, rays, and angles with different measures. Use known angle measures to measure unknown angles. Compare decimals by reasoning about their size. Use fractions or decimals to solve word problems involving money. Solve problems involving line plots and fractions. Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Decompose a fraction or mixed number into a sum of fractions in more than one way. Use tools such as fraction strips, area models, and number lines to subtract fractions. Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Use the four operations to solve problems involving time. Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Use appropriate tools strategically. Use appropriate tools strategically. Model with mathematics. Model with mathematics. Attend to precision. Attend to precision. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Identify and estimate angles and their measure. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe intersecting, parallel, and perpendicular lines. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole- number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Know relative sizes of measurement units. Solve problems involving metric measurement. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two-dimensional figure. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Look for and make use of structure. Look for and make use of structure. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two- dimensional shapes by their sides and/or angles. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Measure and sketch angles in whole-number degrees using a protractor. Draw and measure angles in whole-number degrees using a protractor. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Solve problems involving the conversion of one measure of time to another. Solve word problems involving addition and subtraction of time intervals that cross the hour. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. Online End-of-Year Assessment Curriculum Standards: Attend to precision. Make sense of problems and persevere in solving them. Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Use models or rename fractions to compare. Read and interpret data using line plots. Find the unknown length or width of a rectangle using the known area or perimeter. Use previously- learned concepts and skills to represent and solve problems. Use the standard algorithm to multiply 4- digit numbers by 1-digit numbers. Use addition and subtraction to solve problems with unknown angle measures. Use multiplication and division to compare two quantities. Use the structure of the place- value system for decimals to solve problems. Classify triangles by line segments and angles. Classify quadrilaterals by lines and angles. Recognize and draw lines, rays, and angles with different measures. Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Use fractions or decimals to solve word problems involving money. Add and subtract whole numbers mentally using a variety of methods. Use place value to round multi-digit numbers. Use multiplication to find multiples of a given number. Solve problems involving separating parts of the same whole by subtracting fractions. Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. Solve two-step problems by finding and solving the hidden question first. Use compatible numbers to estimate quotients. Use repeated reasoning to generalize how to solve problems that are similar. Solve division problems and interpret remainders. Use multiplication to find all the factor pairs for a whole number. Use the four operations to solve problems involving time. Construct arguments about fractions. Use equivalent fractions and properties of operations to add mixed numbers with like denominators. Attend to precision. Attend to precision. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input- output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create an input/output chart or table to represent or extend a numerical pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two- dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Model with mathematics. Model with mathematics. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one- digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Find whole-number quotients and remainders with up to three-digit dividends and one- digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. The student will read, write, represent, and identify decimals expressed through thousandths. Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Round decimals to the nearest tenth. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Look for and make use of structure. Look for and make use of structure. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Round multi-digit whole numbers to any place. Find all factor pairs for a whole number in the range 1– 100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. The student will estimate and determine quotients of whole numbers, with and without remainders. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Interpret remainders in word problems. Solve problems involving the conversion of one measure of time to another. Solve word problems involving addition and subtraction of time intervals that cross the hour. The student will compare and order fractions and mixed numbers, with and without models. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. Topic 17: Step-Up to Grade 5 17-1: Understand Decimal Place Value Student's Edition eText: Grade 4 Lesson 17-1 Interactive Student Edition: Grade 4 Lesson 17-1 Develop: Problem-Based Learning Understand Decimal Place Value: Solve & Share Curriculum Standards: Read and write decimals through thousandths in different ways. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names and expanded form (e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)). Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Read, write, and compare decimals to thousandths. Write decimals using base-ten numerals, number names, and expanded form. Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. Develop: Visual Learning Understand Decimal Place Value: Visual Learning Curriculum Standards: Read and write decimals through thousandths in different ways. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names and expanded form (e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)). Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Read, write, and compare decimals to thousandths. Write decimals using base-ten numerals, number names, and expanded form. Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. Understand Decimal Place Value: Convince Me! Curriculum Standards: Read and write decimals through thousandths in different ways. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names and expanded form (e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)). Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Read, write, and compare decimals to thousandths. Write decimals using base-ten numerals, number names, and expanded form. Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. Understand Decimal Place Value: Practice 17-2: Compare Decimals Student's Edition eText: Grade 4 Lesson 17-2 Interactive Student Edition: Grade 4 Lesson 17-2 Develop: Problem-Based Learning Compare Decimals: Solve & Share Curriculum Standards: Use place value to compare decimals through thousandths. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. Compare and order fractions and or decimals to the thousandths place using the symbols >, = or <, and justify the solution. Develop: Visual Learning Compare Decimals: Visual Learning Curriculum Standards: Use place value to compare decimals through thousandths. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. Compare and order fractions and or decimals to the thousandths place using the symbols >, = or <, and justify the solution. Compare Decimals: Convince Me! Curriculum Standards: Use place value to compare decimals through thousandths. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. Compare and order fractions and or decimals to the thousandths place using the symbols >, = or <, and justify the solution. Compare Decimals: Practice 17-3: Use Models to Add and Subtract Decimals Student's Edition eText: Grade 4 Lesson 17-3 Interactive Student Edition: Grade 4 Lesson 17-3 Develop: Problem-Based Learning Use Models to Add and Subtract Decimals: Solve & Share Use Models to Add and Subtract Decimals: Solve & ShareThis interactive component provides the Solve & Share problem from the student edition in an interactive format. It is designed for whole-class instruction. Curriculum Standards: Model sums and differences of decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. Develop: Visual Learning Use Models to Add and Subtract Decimals: Visual Learning Curriculum Standards: Model sums and differences of decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. Use Models to Add and Subtract Decimals: Convince Me! Curriculum Standards: Model sums and differences of decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. Use Models to Add and Subtract Decimals: Practice 17-4: Estimate the Product of a Decimal and a Whole Number Student's Edition eText: Grade 4 Lesson 17-4 Interactive Student Edition: Grade 4 Lesson 17-4 Develop: Problem-Based Learning Estimate the Product of a Decimal and a Whole Number: Solve & Share Curriculum Standards: Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Develop: Visual Learning Estimate the Product of a Decimal and a Whole Number: Visual Learning Curriculum Standards: Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Estimate the Product of a Decimal and a Whole Number: Convince Me! Curriculum Standards: Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Estimate the Product of a Decimal and a Whole Number: Practice 17-5: Find Common Denominators Student's Edition eText: Grade 4 Lesson 17-5 Interactive Student Edition: Grade 4 Lesson 17-5 Develop: Problem-Based Learning Find Common Denominators: Solve & Share Curriculum Standards: Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi- step problems involving variables, whole numbers, fractions and decimals. Develop: Visual Learning Find Common Denominators: Visual Learning Curriculum Standards: Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi- step problems involving variables, whole numbers, fractions and decimals. Find Common Denominators: Convince Me! Curriculum Standards: Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi- step problems involving variables, whole numbers, fractions and decimals. Find Common Denominators: Practice 17-6: Add Fractions with Unlike Denominators Interactive Student Edition: Grade 4 Lesson 17-6 17-7: Subtract Fractions with Unlike Denominators Student's Edition eText: Grade 4 Lesson 17-7 Interactive Student Edition: Grade 4 Lesson 17-7 Develop: Problem-Based Learning Subtract Fractions with Unlike Denominators: Solve & Share Curriculum Standards: Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. Develop: Visual Learning Subtract Fractions with Unlike Denominators: Visual Learning Curriculum Standards: Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. Subtract Fractions with Unlike Denominators: Convince Me! Curriculum Standards: Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. Subtract Fractions with Unlike Denominators: Practice 17-8: Multiply Fractions and Whole Numbers Student's Edition eText: Grade 4 Lesson 17-8 Interactive Student Edition: Grade 4 Lesson 17-8 Develop: Problem-Based Learning Multiply Fractions and Whole Numbers: Solve & Share Curriculum Standards: Multiply fractions and whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. (e.g., Use a visual fraction model to show (2/3) × 4 = 8/3 and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. Develop: Visual Learning Multiply Fractions and Whole Numbers: Visual Learning Curriculum Standards: Multiply fractions and whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. (e.g., Use a visual fraction model to show (2/3) × 4 = 8/3 and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. Multiply Fractions and Whole Numbers: Convince Me! Curriculum Standards: Multiply fractions and whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. (e.g., Use a visual fraction model to show (2/3) × 4 = 8/3 and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. Multiply Fractions and Whole Numbers: Practice 17-9: Divide Whole Numbers by Unit Fractions Student's Edition eText: Grade 4 Lesson 17-9 Interactive Student Edition: Grade 4 Lesson 17-9 Develop: Problem-Based Learning Divide Whole Numbers by Unit Fractions: Solve & Share Curriculum Standards: Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a whole number by a unit fraction and compute such quotients. (e.g., Create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. (e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many1/3-cup servings are in 2 cups of raisins?) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. Calculate and interpret the quotient of a unit fraction by a non-zero whole number. Calculate and interpret the quotient of a whole number by a unit fraction. Develop: Visual Learning Divide Whole Numbers by Unit Fractions: Visual Learning Curriculum Standards: Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a whole number by a unit fraction and compute such quotients. (e.g., Create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. (e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many1/3-cup servings are in 2 cups of raisins?) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. Calculate and interpret the quotient of a unit fraction by a non-zero whole number. Calculate and interpret the quotient of a whole number by a unit fraction. Divide Whole Numbers by Unit Fractions: Convince Me! Curriculum Standards: Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a whole number by a unit fraction and compute such quotients. (e.g., Create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. (e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many1/3-cup servings are in 2 cups of raisins?) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. Calculate and interpret the quotient of a unit fraction by a non-zero whole number. Calculate and interpret the quotient of a whole number by a unit fraction. Divide Whole Numbers by Unit Fractions: Practice 17-10: Model Volume Student's Edition eText: Grade 4 Lesson 17-10 Interactive Student Edition: Grade 4 Lesson 17-10 Develop: Problem-Based Learning Model Volume: Solve & Share Curriculum Standards: Find the volume of solid figures. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. Understand the concept of volume and recognize that volume is measured in cubic units. Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. Analyze and describe the properties of prisms and pyramids. Develop: Visual Learning Model Volume: Visual Learning Curriculum Standards: Find the volume of solid figures. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. Understand the concept of volume and recognize that volume is measured in cubic units. Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. Analyze and describe the properties of prisms and pyramids. Model Volume: Convince Me! Curriculum Standards: Find the volume of solid figures. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. Understand the concept of volume and recognize that volume is measured in cubic units. Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. Analyze and describe the properties of prisms and pyramids. Model Volume: Practice Online 3/4-Year Practice Performance Tasks Online 3/4-Year Practice Performance Task 1 Online 3/4-Year Practice Performance Task 2 Online Next Generation Assessment Practice Test Math Diagnosis and Intervention System 2.0 Booklet A: Numbers, Place Value, Money, and Patterns in Grades K-3 A1: Zero to Five Curriculum Standards: Use math to explain what you know about counting. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted. Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. The student will tell how many are in a given set of 20 or fewer objects by counting orally. The student will read, write, and represent numbers from 0 through 20. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Count, with and without objects, forward and backward to at least 20. Recognize that a number can be used to represent how many objects are in a set up to 10. Count forward, with and without objects, from any given number up to 10. Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives. Construct viable arguments and critique the reasoning of others. Compare groups by counting. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching and counting strategies). Compare two numbers between 1 and 10 presented as written numerals. The student, given no more than three sets, each set containing 10 or fewer concrete objects, will compare and describe one set as having more, fewer, or the same number of objects as the other set(s). Compare and order whole numbers, with and without objects, from 0 to 20. Using the words more than, less than or equal to compare and order whole numbers, with and without objects, from 0 to 10. Identify whether the number of objects, within 10, in one group is greater than, less than, or equal to the number of objects in another group, by using matching and counting strategies. Compare two numbers, within 10, presented as written numerals. Construct viable arguments and critique the reasoning of others. Compare two or more sets of objects and identify which set is equal to, more than or less than the other. Compare two numerals, between 1 and 10, and determine which is more than or less than the other. Compare category counts using appropriate language. A2: More and Fewer A3: Six to Ten Curriculum Standards: Count to the numbers 6 and 7. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. The student will tell how many are in a given set of 20 or fewer objects by counting orally. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Count, with and without objects, forward and backward to at least 20. Count aloud forward in sequence to 100 by 1’s and 10’s. Recognize that a number can be used to represent how many objects are in a set up to 10. Count forward, with and without objects, from any given number up to 10. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object (one-to-one correspondence). Given a number from 1–20, count out that many objects. Read and write the numbers 6 and 7. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. The student will read, write, and represent numbers from 0 through 20. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. Given 10 objects in a scattered arrangement, identify how many. Count to the numbers 8 and 9. Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Count forward beginning from a given number between 1 and 20. Read and write numerals and represent a number of objects from 0 to 20. Demonstrate that a number can be used to represent “how many” are in a set. A4: Ordinal Numbers Through Tenth A5: Spatial Patterns for Numbers to 10 A6: Comparing Numbers A7: Comparing Numbers to 10 A8: Numbers to 12 Curriculum Standards: Count and write numbers 11 and 12. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1– 20, count out that many objects. The student will tell how many are in a given set of 20 or fewer objects by counting orally. The student will read, write, and represent numbers from 0 through 20. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Count, with and without objects, forward and backward to at least 20. Count aloud forward in sequence to 100 by 1’s and 10’s. Count to the numbers 8 and 9. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Count forward, with and without objects, from any given number up to 10. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object (one-to-one correspondence). Given a number from 1–20, count out that many objects. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. Given 10 objects in a scattered arrangement, identify how many. Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Count forward beginning from a given number between 1 and 20. Read and write numerals and represent a number of objects from 0 to 20. Demonstrate that a number can be used to represent “how many” are in a set. A9: Ordering Numbers to 12 with a Number Line A10: 11 to 19 Curriculum Standards: Count and write numbers 13, 14, and 15. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1– 20, count out that many objects. The student will tell how many are in a given set of 20 or fewer objects by counting orally. The student will read, write, and represent numbers from 0 through 20. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Count, with and without objects, forward and backward to at least 20. Count aloud forward in sequence to 100 by 1’s and 10’s. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. Given a number from 1– 20, count out that many objects. Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. Given 10 objects in a scattered arrangement, identify how many. Count forward beginning from a given number between 1 and 20. Read and write numerals and represent a number of objects from 0 to 20. Demonstrate that a number can be used to represent “how many” are in a set. A11: Number Words to Twenty A12: Numbers to 30 A13: Counting to 100 Curriculum Standards: Count by tens and ones from any number up to 100. Count to 100 by ones and by tens. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). The student will count forward orally by ones from 0 to 100. Count, with and without objects, forward and backward to at least 20. Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ?, ??, ???. Count aloud forward in sequence to 100 by 1’s and 10’s. Counting to 100 by ones. Counting to 100 by tens. Count forward beginning from a given number within the known sequence, instead of having to begin at 1. Count to 100 by ones and tens. Count forward beginning from a given number between 1 and 20. A14: Counting Backward from 20 A15: Counting Backward from 100 A16: Counting by 10s to 100 Curriculum Standards: Skip count by tens to 100. Count to 100 by ones and by tens. The student will count forward by tens to determine the total number of objects to 100. Show groups of 10 with connecting cubes. 10 can be thought of as a bundle of ten ones — called a “ten.” (e.g., A group of ten pennies is equivalent to a dime.) The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight or nine tens (and 0 ones). The student will count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110. The student, given up to 110 objects, will group a collection into tens and ones and write the corresponding numeral. Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Count, with and without objects, forward and backward from any given number up to 120. Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Add 2 multiples of 10. Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two- digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. Find a number that is 10 more or 10 less than a given number. Use words, pictures, objects, length- based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Count, with and without objects, forward and backward to at least 20. Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ?, ??, ???. Count aloud forward in sequence to 100 by 1’s and 10’s. Counting to 100 by ones. Counting to 100 by tens. Unitize by making a ten from a collection of ten ones. Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens, with 0 ones. A two-digit number and a one-digit number A two- digit number and a multiple of 10 Read and write numerals and represent a number of objects with a written numeral. Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”. Understand two-digit numbers are composed of ten(s) and one(s). Add within 100. Count to 100 by ones and tens. A17: Using Numbers 11 to 20 A18: Making Numbers 11 to 20 Curriculum Standards: Make the numbers 17, 18, and 19. Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones (one ten) and one, two, three, four, five, six, seven, eight, or nine ones. The student will tell how many are in a given set of 20 or fewer objects by counting orally. The student will investigate and describe part-whole relationships for numbers up to 10. Read and write numbers 11 to 19. 10 can be thought of as a bundle of ten ones — called a “ten.” (e.g., A group of ten pennies is equivalent to a dime.) The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight or nine ones. The student, given up to 110 objects, will group a collection into tens and ones and write the corresponding numeral. Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Count, with and without objects, forward and backward from any given number up to 120. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Count, with and without objects, forward and backward to at least 20. Compose and decompose numbers up to 10 with objects and pictures. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. Using objects or drawings. Recording each composition or decomposition by a drawing or expression. Understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Unitize by making a ten from a collection of ten ones. Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Read and write numerals and represent a number of objects with a written numeral. Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”. Understand two-digit numbers are composed of ten(s) and one(s). A19: Counting from any Number Curriculum Standards: Count forward from any number to a number within 20. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Understand that each successive number name refers to a quantity that is one larger. The student will count forward orally by ones from 0 to 100. Count by 1s to 120. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. The student will count forward orally by ones to 110, starting at any number between 0 and 110. The student will write the numerals 0 to 110 in sequence and out-of-sequence. Count, with and without objects, forward and backward from any given number up to 120. Find a number that is 10 more or 10 less than a given number. Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s. Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. Count, with and without objects, forward and backward to at least 20. Find a number that is 1 more or 1 less than a given number. Count aloud forward in sequence to 100 by 1’s and 10’s. Count forward beginning from a given number within the known sequence, instead of having to begin at 1. Given up to 20 objects, name the next successive number when an object is added, recognizing the quantity is one more/greater. Count to 150, starting at any number less than 150. Read and write numerals, and represent a number of objects with a written numeral, to 100. Count to 120, starting at any number less than 120. Read and write numerals and represent a number of objects with a written numeral. Count forward beginning from a given number between 1 and 20. Demonstrate that each successive number name refers to a quantity that is one larger than the previous number. A20: Using Skip Counting A21: Odd and Even Curriculum Standards: Tell if a group of objects is even or odd. Use knowledge of even and odd numbers to identify multiplication patterns. Use different ways to tell if a group of objects shows an even or odd number. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. The student will use objects to determine whether a number is even or odd. The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Pairing objects, then counting them by 2s. Determining whether objects can be placed into two equal groups. Writing an equation to express an even number as a sum of two equal addends. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Demonstrate fluency with addition and subtraction within 20. Determine if a set of objects has an odd or even number of members. Count by 2s to 100 starting with any even number. Express even numbers as pairings or groups of 2, and write an expression to represent the number using addends of 2. Express even numbers as being composed of equal groups and write an expression to represent the number with 2 equal addends. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. A22: Before, After, and Between A23: Counting with Tens and Ones Curriculum Standards: Use drawings to solve problems with tens and ones. Understand the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: The student, given up to 110 objects, will group a collection into tens and ones and write the corresponding numeral. Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Count, with and without objects, forward and backward from any given number up to 120. Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand two-digit numbers are composed of ten(s) and one(s). A24: Tens Curriculum Standards: Find better and faster ways to solve problems. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. The student will count forward orally by ones to 110, starting at any number between 0 and 110. The student will write the numerals 0 to 110 in sequence and out-of-sequence. The student will count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110. Count, with and without objects, forward and backward from any given number up to 120. Find a number that is 10 more or 10 less than a given number. Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s. Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. A25: Tens and Ones Curriculum Standards: Break apart numbers into tens and ones to find their sum. Break apart addends and combine them in different ways to make numbers that are easy to add mentally. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. Use drawings to solve problems with tens and ones. Understand the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: The student, given up to 110 objects, will group a collection into tens and ones and write the corresponding numeral. Add within 100 using place-value strategies. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two- digit numbers. Apply commutative and identity properties and number sense to find values for unknowns that make number sentences involving addition and subtraction true or false. Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Count, with and without objects, forward and backward from any given number up to 120. Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use tens and ones to make numbers in different ways. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Comparing addition and subtraction strategies, and explaining why they work. Understand that the two digits of a two-digit number represent amounts of tens and ones. Look for and make use of structure. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Understand two-digit numbers are composed of ten(s) and one(s). Look for and make use of structure. A26: Number Patterns to 100 Curriculum Standards: Use patterns to count to 30. Count to 100 by ones and by tens. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). The student will count forward orally by ones from 0 to 100. Use place-value blocks to compare 2 two- digit numbers. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. The student, given up to 110 objects, will compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Compare and order whole numbers up to 100. Use words to describe the relative size of numbers. Compare and order whole numbers from 0 to 100. Use objects to represent and use words to describe the relative size of numbers, such as more than, less than, and equal to. Count, with and without objects, forward and backward to at least 20. Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ?, ??, ???. Count aloud forward in sequence to 100 by 1’s and 10’s. Counting to 100 by ones. Counting to 100 by tens. Count forward beginning from a given number within the known sequence, instead of having to begin at 1. Compare two two-digit numbers based on the value of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Compare two two-digit numbers using the symbols >, = or <. Count to 100 by ones and tens. Count forward beginning from a given number between 1 and 20. A27: 1 More or Less, 10 More or Less Curriculum Standards: Use mental math to add tens to two-digit numbers. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count and explain the reasoning used. The student, given a familiar problem situation involving magnitude, will select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, 500). The student will demonstrate an understanding of equality through the use of the equal symbol. Find a number that is 10 more or 10 less than a given number. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Find a number that is 10 more or 10 less than a given number up to 100. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Calculate 10 more or 10 less than a given number mentally without having to count. A28: Using >, <, and = to Compare Numbers Curriculum Standards: Compare two numbers using a greater than, a less than, or an equal to sign. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. The student, given up to 110 objects, will compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Compare and order whole numbers up to 100. Use words to describe the relative size of numbers. Compare and order whole numbers from 0 to 100. Use objects to represent and use words to describe the relative size of numbers, such as more than, less than, and equal to. Compare two two-digit numbers based on the value of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Compare two two-digit numbers using the symbols >, = or <. A29: Ordering Three Numbers A30: Number Words A31: Numbers to 100 on the Number Line A32: Counting by Hundreds Curriculum Standards: Understand place value and count by hundreds to 1,000. Make and name a number in different ways to show the same value. 100 can be thought of as a bundle of ten tens – called a “hundred.” Numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight or nine hundreds, and 0 tens and 0 ones. The student will read, write, and identify the place and value of each digit in a three-digit numeral, with and without models. Read and write numbers to 1000 using base-ten numerals, number names and expanded form. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds. Unitize by making a hundred from a collection of ten tens. Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds, with 0 tens and 0 ones. Compose and decompose numbers using various groupings of hundreds, tens, and ones. Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. Understand three-digit numbers are composed of hundreds, tens and ones. Understand that 100 can be thought of as 10 tens – called a “hundred”. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. A33: Building Numbers to 999 Curriculum Standards: Read and write 3-digit numbers in expanded form, standard form, and word form. Make and name a number in different ways to show the same value. Use place-value blocks and drawings to model and write 3-digit numbers. Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). Understand the following as special cases: Read and write numbers to 1000 using base-ten numerals, number names and expanded form. The student will read, write, and identify the place and value of each digit in a three-digit numeral, with and without models. 100 can be thought of as a bundle of ten tens – called a “hundred.” Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Unitize by making a hundred from a collection of ten tens. Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds, with 0 tens and 0 ones. Compose and decompose numbers using various groupings of hundreds, tens, and ones. Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. Understand three-digit numbers are composed of hundreds, tens and ones. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Understand that 100 can be thought of as 10 tens – called a “hundred”. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. A34: Reading and Writing Numbers to 999 Curriculum Standards: Read and write 3-digit numbers in expanded form, standard form, and word form. Make and name a number in different ways to show the same value. Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). Understand the following as special cases: Read and write numbers to 1000 using base-ten numerals, number names and expanded form. The student will read, write, and identify the place and value of each digit in a three-digit numeral, with and without models. 100 can be thought of as a bundle of ten tens – called a “hundred.” Tell the value of a digit by where it is placed in a number. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Unitize by making a hundred from a collection of ten tens. Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds, with 0 tens and 0 ones. Compose and decompose numbers using various groupings of hundreds, tens, and ones. Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. Understand three-digit numbers are composed of hundreds, tens and ones. Understand that 100 can be thought of as 10 tens – called a “hundred”. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base- ten numerals and expanded form. Add or subtract within 1000, and justify the solution. A35: Patterns with Numbers on Hundreds Charts Curriculum Standards: Use place-value patterns to mentally count by 1s and 10s from a given number. Add 10 or 100 mentally using place value. Use an open number line to add 3-digit numbers. Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number 100-900. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Count within 1000 and skip-count by 5s, 10s and 100s. The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. Represent, create, describe, complete, and extend growing and shrinking patterns with quantity and numbers in a variety of real-world and mathematical contexts. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Concrete models or drawings Strategies based on place value Properties of operations Count within 1000; skip-count by 5s, 10s, and 100s. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. Add or subtract mentally 10 or 100 to or from a given number within 1000. Demonstrate fluency with addition and subtraction within 100. A36: Comparing Numbers to 999 Curriculum Standards: Compare numbers using place value. Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers between 0 and 999. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Compare and order whole numbers up to 1000. Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g., 425 > 276, 73 < 107, page 351 comes after page 350, 753 is between 700 and 800). Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Compare two three-digit numbers using the symbols >, = or <. A37: Before, After, and Between A38: Ordering Numbers to 999 A39: Numbers to 999 on the Number Line Curriculum Standards: Use an open number line to count back to subtract 3-digit numbers. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Concrete models or drawings Strategies based on place value Properties of operations Relationship between addition and subtraction Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. A40: Skip Counting on the Number Line Curriculum Standards: Skip count by 5s, 10s, and 100s using a number line. Count within 1000 and skip-count by 5s, 10s and 100s. The student will identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999. The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. Represent, create, describe, complete, and extend growing and shrinking patterns with quantity and numbers in a variety of real-world and mathematical contexts. Count within 1000; skip-count by 5s, 10s, and 100s. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. A41: Ways to Show Numbers Curriculum Standards: Read and write 3-digit numbers in expanded form, standard form, and word form. Make and name a number in different ways to show the same value. Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). Understand the following as special cases: Read and write numbers to 1000 using base-ten numerals, number names and expanded form. The student will read, write, and identify the place and value of each digit in a three-digit numeral, with and without models. 100 can be thought of as a bundle of ten tens – called a “hundred.” Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines and manipulatives. Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Unitize by making a hundred from a collection of ten tens. Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds, with 0 tens and 0 ones. Compose and decompose numbers using various groupings of hundreds, tens, and ones. Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. Understand three-digit numbers are composed of hundreds, tens and ones. Understand that 100 can be thought of as 10 tens – called a “hundred”. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. A42: Place-Value Patterns A43: Reading and Writing 4-Digit Numbers A44: Comparing and Ordering Numbers A45: Rounding to the Nearest Ten and Hundred Curriculum Standards: Use place value and a number line to round numbers. Use place value understanding to round whole numbers to the nearest 10 or 100. The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Round whole numbers to the nearest 10 or 100. A46: Numbers Halfway Between and Rounding A47: Equal Parts Curriculum Standards: Determine whether shapes are divided into equal shares. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares and understand for these examples that decomposing into more equal shares creates smaller shares. The student will represent and solve practical problems involving equal sharing with two or four sharers. The student will represent and name fractions for halves and fourths, using models. Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. Partition a regular polygon using physical models and recognize when those parts are equal. Partition circles and rectangles into two and four equal shares. Describe the whole as two of, or four of the shares. Explain that decomposing into more equal shares creates smaller shares. Partition circles and rectangles into two or four equal shares, and describe the shares and the wholes verbally. A48: Understanding Fractions to Fourths Curriculum Standards: Divide circles and rectangles into halves, thirds, and fourths. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. The student will name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths. The student will represent fractional parts with models and with symbols. Divide shapes into 2 and 4 equal shares and use words to describe those shares. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares and understand for these examples that decomposing into more equal shares creates smaller shares. The student will represent and solve practical problems involving equal sharing with two or four sharers. The student will represent and name fractions for halves and fourths, using models. Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. Partition a regular polygon using physical models and recognize when those parts are equal. Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, fourths, fourth of, quarter of. Describe the whole as two halves, three thirds, four fourths. Explain that equal shares of identical wholes need not have the same shape. Partition circles and rectangles into two and four equal shares. Describe the shares as halves and fourths, as half of and fourth of. Describe the whole as two of, or four of the shares. Explain that decomposing into more equal shares creates smaller shares. Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole. Demonstrate that equal shares of identical wholes need not have the same shape. Partition circles and rectangles into two or four equal shares, and describe the shares and the wholes verbally. A49: Halves A50: Fractions of a Set A51: Estimating Fractional Amounts Curriculum Standards: Use benchmark numbers to compare fractions. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, = or < and justify the conclusions (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ?), with models. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Use models and number lines to order and compare fractions that are related to the same whole. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths. Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. Compare two fractions with the same numerator or denominator using the symbols >, = or <, and justify the solution. Explain why fraction comparisons are only valid when the two fractions refer to the same whole. A52: Equal Parts of a Whole Curriculum Standards: Divide circles and rectangles into halves, thirds, and fourths. Understand how to read and write unit fractions for equal-size parts of a region. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. The student will name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths. The student will represent fractional parts with models and with symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. Read and write fractions with words and symbols. Construct fractions using length, set, and area models. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, fourths, fourth of, quarter of. Describe the whole as two halves, three thirds, four fourths. Explain that equal shares of identical wholes need not have the same shape. Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; Explain that a unit fraction is one of those parts. Represent and identify unit fractions using area and length models. Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction. Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole. Demonstrate that equal shares of identical wholes need not have the same shape. Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole. Describe the numerator as representing the number of pieces being considered. Describe the denominator as the number of pieces that make the whole. Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. A53: Parts of a Region Curriculum Standards: Use a fraction to represent multiple copies of a unit fraction. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Read and write fractions with words and symbols. Construct fractions using length, set, and area models. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; Explain that a unit fraction is one of those parts. Represent and identify unit fractions using area and length models. Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction. Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole. Describe the numerator as representing the number of pieces being considered. Describe the denominator as the number of pieces that make the whole. Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. A54: Parts of a Set A55: Fractions on the Number Line A56: Fractions and Length Curriculum Standards: Represent fractions on a number line. Represent fractions greater than 1 on a number line. Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (e.g., Given that b parts is 4 parts, then 1/b represents 1/4. Students partition the number line into fourths and locate 1/4 on the number line.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (e.g., Given that a/b represents 3/4 or 6/4, students partition the number line into fourths and represent these fractions accurately on the same number line; students extend the number line to include the number of wholes required for the given fractions.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Construct fractions using length, set, and area models. Represent and identify unit fractions using area and length models. Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Represent fractions on a number line. Understand the whole is the interval from 0 to 1. Understand the whole is partitioned into equal parts. Understand a fraction represents the endpoint of the length a given number of partitions from 0. A57: Using Models to Compare Fractions Curriculum Standards: Use models such as fraction strips to compare fractions that refer to the same whole and have the same denominator. Use models such as fraction strips to compare fractions that refer to the same whole and have the same numerator. Construct math arguments using fractions. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, = or < and justify the conclusions (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ?), with models. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Construct fractions using length, set, and area models. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. Use models and number lines to order and compare fractions that are related to the same whole. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths. Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. Compare two fractions with the same numerator or denominator using the symbols >, = or <, and justify the solution. Explain why fraction comparisons are only valid when the two fractions refer to the same whole. A58: Comparing Fractions on the Number Line A59: Using Models to Find Equivalent Fractions Curriculum Standards: Find equivalent fractions that name the same part of the whole. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Construct fractions using length, set, and area models. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line. Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. A60: Comparing Fractions A61: Money A62: Pennies and Nickels Curriculum Standards: Solve problems with coins. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Determine the value of a collection(s) of coins up to one dollar using the cent symbol. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. A63: Dimes Curriculum Standards: Solve problems with coins. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Determine the value of a collection(s) of coins up to one dollar using the cent symbol. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. A64: Counting Pennies, Nickels, and Dimes Curriculum Standards: Solve problems with coins. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Determine the value of a collection(s) of coins up to one dollar using the cent symbol. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. A65: Quarters Curriculum Standards: Solve problems with coins. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Determine the value of a collection(s) of coins up to one dollar using the cent symbol. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. A66: Half-Dollars Curriculum Standards: Solve problems with coins. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Determine the value of a collection(s) of coins up to one dollar using the cent symbol. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. A67: Counting Sets of Coins Curriculum Standards: Solve problems with coins. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Determine the value of a collection(s) of coins up to one dollar using the cent symbol. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. A68: Ways to Show the Same Amount A69: Dollars A70: Counting Money A71: Find a Rule A72: Input/Output Tables A73: Geometric Growth Patterns A74: Place Value Through Thousands A75: Rounding Numbers Through Thousands A76: Comparing and Ordering Numbers Through Thousands A77: Rounding Numbers Through Millions A78: Equality and Inequality A79: Using the Distributive Property Curriculum Standards: Use the Distributive Property to solve problems involving multiplication within 100. Use the multiplication table and the Distributive Property to find patterns in factors and products. Use properties of multiplication to find products when one factor is a multiple of 10. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Demonstrate fluency of multiplication facts with factors up to 10. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Use multiplication and division within 100 to solve problems. Demonstrate fluency with products within 100. Identify arithmetic patterns and explain the patterns using properties of operations. Multiply whole numbers by multiples of 10 in the range 10-90. A80: Working with Unit Fractions A81: Equivalent Fractions A82: Fractions and Division A83: Equivalent Fractions and the Number Line Curriculum Standards: Represent equivalent fractions on a number line. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Construct fractions using length, set, and area models. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line. Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. A84: Counting Coins and Bills A85: Ways to Make 5 Curriculum Standards: Use patterns to add numbers together. Fluently add and subtract within 5. The student will recognize and describe with fluency part-whole relationships for numbers up to 5. The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Recognize and combine groups with totals up to 5 (conceptual subitizing). Demonstrate fluency with addition and subtraction within 5. Recognize, without counting, the quantity of groups up to 5 objects arranged in common patterns. Demonstrate fluency for addition and subtraction within 5. A86: Equal Groups A87: Ways to Make 10 Curriculum Standards: Find number partners for 10. For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation. The student will investigate and describe part-whole relationships for numbers up to 10. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Compose and decompose numbers up to 10 with objects and pictures. Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, or expressions. For any number from 0 to 10, find the number that makes 10 when added to the given number using objects or drawings, and record the answer with a drawing or expression. Make 10 for any number from 1 to 9. A88: Making Numbers With 10 A89: Count on an Open Number Line Curriculum Standards: Count to 120 using an open number line. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. The student will count forward orally by ones to 110, starting at any number between 0 and 110. The student will write the numerals 0 to 110 in sequence and out-of-sequence. Count, with and without objects, forward and backward from any given number up to 120. Find a number that is 10 more or 10 less than a given number. Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s. Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. Count to 150, starting at any number less than 150. Read and write numerals, and represent a number of objects with a written numeral, to 100. Count to 120, starting at any number less than 120. Read and write numerals and represent a number of objects with a written numeral. Count by 10s to 120 starting at any number. A90: Arrays and Repeated Addition Curriculum Standards: Find the total number of objects in a set of rows and columns. Make arrays with equal rows or equal columns to solve addition problems. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. The student will determine sums and differences, using various methods. The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Use concrete models and structured arrangements, such as repeated addition, arrays and ten frames to develop understanding of multiplication. Use objects and number lines to represent number sentences. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Demonstrate fluency with addition and subtraction within 20. Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. A91: Working with Dollar Bills Curriculum Standards: Solve problems with dollar bills and coins that model 100 cents. Solve problems with dollar bills. Count within 1000 and skip-count by 5s, 10s and 100s. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use a combination of coins to represent a given amount of money up to one dollar. Identify quarters, dimes, and nickels and relate their values to pennies. Count within 1000; skip-count by 5s, 10s, and 100s. Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. Whole dollar amounts, using the $ symbol appropriately. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Know the value of a penny, nickel, dime and quarter. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately. Find combinations of coins that equal a given amount. Identify pennies, nickels, dimes and quarters. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. A92: Understand the Whole Curriculum Standards: Determine and draw the whole (unit) given one part (unit fraction). Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. (e.g., Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Read and write fractions with words and symbols. Construct fractions using length, set, and area models. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. Explaining that a fraction with the same numerator and denominator equals one whole. Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. Represent fractions on a number line. Understand the whole is the interval from 0 to 1. Understand the whole is partitioned into equal parts. Understand a fraction represents the endpoint of the length a given number of partitions from 0. A93: Comparing Fractions on a Number Line Curriculum Standards: Use a number line to compare fractions. Construct math arguments using fractions. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, = or < and justify the conclusions (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will represent fractions and mixed numbers with models and symbols. The student will compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ?), with models. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Use models and number lines to order and compare fractions that are related to the same whole. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths. Construct viable arguments and critique the reasoning of others. Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. Compare two fractions with the same numerator or denominator using the symbols >, = or <, and justify the solution. Explain why fraction comparisons are only valid when the two fractions refer to the same whole. Construct viable arguments and critique the reasoning of others. A94: Whole Numbers and Fractions Curriculum Standards: Use fraction names to represent whole numbers. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. (e.g., Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Understand that the size of a fractional part is relative to the size of the whole. Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. Use models and number lines to order and compare fractions that are related to the same whole. Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. Explaining that a fraction with the same numerator and denominator equals one whole. Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line. Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. Booklet B: Basic Facts in Grades K-3 B1: Addition Curriculum Standards: Show how to make a group of ten. Understand the relationship between numbers and quantities; connect counting to cardinality. Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). The student will investigate and describe part-whole relationships for numbers up to 10. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives. Compose and decompose numbers up to 10 with objects and pictures. Understand the relationship between numbers and quantities. Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, or expressions. Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings, and record each decomposition by a drawing or expression. For any number from 0 to 10, find the number that makes 10 when added to the given number using objects or drawings, and record the answer with a drawing or expression. Count backward from a given number between 10 and 1. Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Demonstrate that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted. Demonstrate that each successive number name refers to a quantity that is one larger than the previous number. Represent addition and subtraction within 10. Decompose numbers less than or equal to 10 in more than one way. Classify objects into given categories; count the number of objects in each category. B2: Subtraction B3: Finding Sums Curriculum Standards: Solve related addition and subtraction equations. Fluently add and subtract within 5. The student will recognize and describe with fluency part-whole relationships for numbers up to 5. The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Recognize and combine groups with totals up to 5 (conceptual subitizing). Demonstrate fluency with addition and subtraction within 5. Recognize, without counting, the quantity of groups up to 5 objects arranged in common patterns. Demonstrate fluency for addition and subtraction within 5. B4: Joining Stories Curriculum Standards: Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use the same addends to write two different equations with the same sum. Apply properties of operations as strategies to add and subtract (e.g., If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known: Commutative Property of Addition. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12: Associative Property of Addition). Instructional Note: Students need not use formal terms for these properties. The student will recognize and describe with fluency part-whole relationships for numbers up to 10. The student will demonstrate fluency with addition and subtraction within 10. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Determine if equations involving addition and subtraction are true. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Demonstrate fluency with basic addition facts and related subtraction facts up to 10. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Apply the commutative and associative properties as strategies for solving addition problems. Demonstrate fluency with addition and subtraction within 20. Use properties as strategies to add and subtract. B5: Stories about Joining B6: Finding Differences Curriculum Standards: Solve related addition and subtraction equations. Fluently add and subtract within 5. The student will recognize and describe with fluency part-whole relationships for numbers up to 5. The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Recognize and combine groups with totals up to 5 (conceptual subitizing). Demonstrate fluency with addition and subtraction within 5. Recognize, without counting, the quantity of groups up to 5 objects arranged in common patterns. Demonstrate fluency for addition and subtraction within 5. B7: Comparing Stories Curriculum Standards: Use addition and subtraction to solve word problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. B8: Separating Stories Curriculum Standards: Show numbers in many ways. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), and acting out situations, verbal explanations, expressions, or equations. The student will investigate and describe part-whole relationships for numbers up to 10. The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Represent addition and subtraction, within 10: Demonstrate understanding of addition and subtraction by making connections among representations. Represent addition and subtraction within 10. B9: Making 6 and 7 Curriculum Standards: Solve word problems by drawing pictures and writing equations. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). The student will create and solve single-step story and picture problems using addition and subtraction within 20. The student will recognize and describe with fluency part-whole relationships for numbers up to 10. The student will demonstrate fluency with addition and subtraction within 10. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Represent and solve real-world and mathematical problems using addition and subtraction up to ten. Demonstrate fluency with basic addition facts and related subtraction facts up to 10. Add to/Take from-Change Unknown Put together/Take Apart-Addend Unknown Compare- Difference Unknown Count backward from a given number between 20 and 1. Use addition and subtraction within 20 to solve problems. B10: Making 8 and 9 Curriculum Standards: Write equations to show the parts of 8 and 9. Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). The student will investigate and describe part-whole relationships for numbers up to 10. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Compose and decompose numbers up to 10 with objects and pictures. Represent addition as adding to a number. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), and acting out situations, verbal explanations, expressions, or equations. The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. Count forward beginning from a given number within the known sequence, instead of having to begin at 1. Represent addition and subtraction, within 10: Demonstrate understanding of addition and subtraction by making connections among representations. Compare two numbers, within 10, presented as written numerals. Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, or expressions. Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings, and record each decomposition by a drawing or expression. Count forward beginning from a given number between 1 and 20. Represent addition and subtraction within 10. Count backward from a given number between 10 and 1. Compare two numerals, between 1 and 10, and determine which is more than or less than the other. Decompose numbers less than or equal to 10 in more than one way. B11: Parts of Ten Curriculum Standards: Write equations to show the parts of 10. Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). The student will investigate and describe part-whole relationships for numbers up to 10. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Compose and decompose numbers up to 10 with objects and pictures. Compare two numbers, within 10, presented as written numerals. Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, or expressions. Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings, and record each decomposition by a drawing or expression. For any number from 0 to 10, find the number that makes 10 when added to the given number using objects or drawings, and record the answer with a drawing or expression. Find number partners for 10. For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation. Make 10 for any number from 1 to 9. Count backward from a given number between 10 and 1. Compare two numerals, between 1 and 10, and determine which is more than or less than the other. Represent addition and subtraction within 10. Decompose numbers less than or equal to 10 in more than one way. B12: Adding Across and Down B13: Adding in any Order Curriculum Standards: Use counting on to add numbers and add numbers in any order. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single- step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B14: Missing Parts Curriculum Standards: Use mental math strategies and models to add more than two numbers. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Add up to four two-digit numbers. Write and solve problems involving addition and subtraction within 100. B15: Finding the Missing Part Curriculum Standards: Make the numbers 14, 15, and 16. Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones (one ten) and one, two, three, four, five, six, seven, eight, or nine ones. The student will tell how many are in a given set of 20 or fewer objects by counting orally. The student will investigate and describe part-whole relationships for numbers up to 10. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Count, with and without objects, forward and backward to at least 20. Compose and decompose numbers up to 10 with objects and pictures. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, or expressions. Using objects or drawings. Recording each composition or decomposition by a drawing or expression. Understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Count forward beginning from a given number between 1 and 20. Compose and decompose numbers from 11 to 19 into sets of tens with additional ones. B16: Relating Addition and Subtraction Curriculum Standards: Think addition to subtract quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use addition facts to 10 to solve subtraction problems. Understand subtraction as an unknown-addend problem (e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., Determine the unknown number that makes the equation true in each of the equations. 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?). The student will recognize and describe with fluency part-whole relationships for numbers up to 10. The student will demonstrate fluency with addition and subtraction within 10. Use addition and subtraction to solve word problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Demonstrate fluency with basic addition facts and related subtraction facts up to 10. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem. Demonstrate fluency with addition and subtraction within 10. Counting on Using the relationship between addition and subtraction Creating equivalent but simpler or known sums Determine the unknown whole number in an addition or subtraction equation involving three whole numbers. Demonstrate fluency with addition and subtraction within 20. One-Step problems: Add to/Take from- Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Write and solve problems involving addition and subtraction within 100. Add within 100. Use addition and subtraction within 20 to solve problems. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Add and subtract within 20. Demonstrate fluency with addition and subtraction within 10. B17: Making 10 on a Ten-Frame Curriculum Standards: Use the strategy of making a ten to add quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B18: Missing Parts of 10 B19: Adding with 0, 1, 2 B20: Adding Doubles Curriculum Standards: Use doubles and near doubles to add quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B21: Using Doubles to Add Curriculum Standards: Use doubles and near doubles to add quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B22: Facts with 5 on a Ten-Frame B23: Subtracting with 0, 1, and 2 B24: Using Doubles to Subtract B25: Thinking Addition to 12 to Subtract Curriculum Standards: Think addition to subtract quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use addition facts to find subtraction facts. Understand subtraction as an unknown-addend problem (e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Compose and decompose numbers up to 12 with an emphasis on making ten. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem. Making ten Decomposing a number leading to a ten Using the relationship between addition and subtraction Creating equivalent but simpler or known sums The relationship between addition and subtraction Demonstrate fluency with addition and subtraction within 20. Add within 100. Use addition and subtraction within 20 to solve problems. Demonstrate that subtraction can be solved as an unknown-addend problem. Add and subtract within 20. B26: Doubles to 18 Curriculum Standards: Memorize doubles facts. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Demonstrate fluency with addition and subtraction within 10. Counting on Decomposing a number leading to a ten Creating equivalent but simpler or known sums Add within 100. Use addition and subtraction within 20 to solve problems. Add and subtract within 20. B27: Using Doubles to Add Curriculum Standards: Use doubles facts to solve doubles-plus-2 facts. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Model problems using equations, drawings, arrays, and bar diagrams. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. The student will determine sums and differences, using various methods. The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use concrete models and structured arrangements, such as repeated addition, arrays and ten frames to develop understanding of multiplication. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Model with mathematics. Counting on Decomposing a number leading to a ten Creating equivalent but simpler or known sums Model with mathematics. Add within 100. Use addition and subtraction within 20 to solve problems. Solve problems that call for addition of three whole numbers whose sum is within 20. Add and subtract within 20. B28: Adding 10 B29: Making 10 to Add 9 Curriculum Standards: Use the strategy of making a ten to add quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B30: Making 10 to Add 7 and 8 Curriculum Standards: Use the strategy of making a ten to add quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B31: Adding Three Numbers Curriculum Standards: Use different strategies to solve word problems with 3 addends. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to add and subtract (e.g., If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known: Commutative Property of Addition. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12: Associative Property of Addition). Instructional Note: Students need not use formal terms for these properties. The student will create and solve single-step story and picture problems using addition and subtraction within 20. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Represent and solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, by using objects, drawings, and equations with a symbol for the unknown number. Apply the commutative and associative properties as strategies for solving addition problems. Use addition and subtraction within 20 to solve problems. Solve problems that call for addition of three whole numbers whose sum is within 20. Use properties as strategies to add and subtract. B32: Stories about Separating B33: Stories about Comparing Curriculum Standards: Use addition and subtraction to solve word problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. B34: Relating Addition and Subtraction to 18 Curriculum Standards: Use addition and subtraction to solve word problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use addition facts to find subtraction facts. Understand subtraction as an unknown-addend problem (e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Think addition to subtract quickly and accurately. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Compose and decompose numbers up to 12 with an emphasis on making ten. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Use the relationship between addition and subtraction to generate basic facts up to 20. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem. Making ten Decomposing a number leading to a ten Using the relationship between addition and subtraction Creating equivalent but simpler or known sums The relationship between addition and subtraction Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. Add within 100. Use addition and subtraction within 20 to solve problems. Demonstrate that subtraction can be solved as an unknown-addend problem. Add and subtract within 20. B35: Fact Families Curriculum Standards: Use addition facts to find subtraction facts. Understand subtraction as an unknown-addend problem (e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Compose and decompose numbers up to 12 with an emphasis on making ten. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem. Making ten Decomposing a number leading to a ten Using the relationship between addition and subtraction Creating equivalent but simpler or known sums The relationship between addition and subtraction Add within 100. Use addition and subtraction within 20 to solve problems. Demonstrate that subtraction can be solved as an unknown-addend problem. Add and subtract within 20. B36: Thinking Addition to Subtract Doubles B37: Using Addition to 18 to Subtract Curriculum Standards: Think addition to subtract quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B38: Subtraction Facts with 10 B39: Using Subtraction Strategies Curriculum Standards: Use addition and subtraction to solve word problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. B40: Using = and ? Curriculum Standards: Determine if addition and subtraction equations are true or false. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false (e.g., Which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2). The student will create and solve single-step story and picture problems using addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Determine if equations involving addition and subtraction are true. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Determine if equations involving addition and subtraction are true. Find the missing numbers in equations to make them true. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., Determine the unknown number that makes the equation true in each of the equations. 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?). Determine the unknown whole number in an addition or subtraction equation involving three whole numbers. Apply understanding of the equal sign to determine if equations involving addition and subtraction are true. Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. B41: Addition Properties Curriculum Standards: Solve real-world problems using properties of addition. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. B42: Relating Addition and Subtraction Curriculum Standards: Think addition to subtract quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B43: Multiplication as Repeated Addition Curriculum Standards: Use repeated addition to show the relationship between multiplication and addition. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. B44: Arrays and Multiplication Curriculum Standards: Use arrays as one way to think about and understand multiplication. Understand and use the Commutative Property of Multiplication. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. B45: Writing Multiplication Stories Curriculum Standards: Use multiplication to write and solve real-world problems involving equal groups. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Recognize the relationship between multiplication and division to represent and solve real-world problems. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Demonstrate fluency with products within 100. B46: Multiplying by 2 and 5 Curriculum Standards: Gain fluency in multiplication when using 2and 5 as factors. Students will use number relationships and patterns to develop reasoning strategies to support their recall of the basic multiplication facts. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Demonstrate fluency of multiplication facts with factors up to 10. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. B47: Multiplying by 9 Curriculum Standards: Gain fluency in multiplication when using 9 as a factor. Students will use number relationships and patterns to develop reasoning strategies to support their recall of the basic multiplication facts. Use strategies such as skip counting and properties of operations to multiply. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Demonstrate fluency of multiplication facts with factors up to 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one- step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. B48: Multiplying by 1 and 0 Curriculum Standards: Gain fluency in multiplication when multiplying by 0 or 1. Students will use number relationships and patterns to develop reasoning strategies to support their recall of the basic multiplication facts. Use strategies such as skip counting and properties of operations to multiply. Use arrays as one way to think about and understand multiplication. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. The student will create equations to represent equivalent mathematical relationships. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Demonstrate fluency of multiplication facts with factors up to 10. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Demonstrate fluency with products within 100. Identify arithmetic patterns and explain the patterns using properties of operations. B49: Multiplying by 10 Curriculum Standards: Gain fluency in multiplication when multiplying by 10. Students will use number relationships and patterns to develop reasoning strategies to support their recall of the basic multiplication facts. Use strategies such as skip counting and properties of operations to multiply. Use different strategies to find products when one factor is a multiple of 10. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Demonstrate fluency of multiplication facts with factors up to 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Multiply whole numbers by multiples of 10 in the range 10-90. B50: Multiplying by 3 Curriculum Standards: Use appropriate tools and the Distributive Property to break apart unknown facts with 3 as a factor. Use strategies such as skip counting and properties of operations to multiply. Use number lines to join equal groups. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will create equations to represent equivalent mathematical relationships. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Demonstrate fluency of multiplication facts with factors up to 10. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. B51: Multiplying by 4 Curriculum Standards: Use the Distributive Property to break apart unknown facts with 4 as a factor. Use strategies such as skip counting and properties of operations to multiply. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Demonstrate fluency of multiplication facts with factors up to 10. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. B52: Multiplying by 6 or 7 Curriculum Standards: Use the Distributive Property to break apart unknown facts with 6 or 7 as a factor. Use strategies such as skip counting and properties of operations to multiply. Understand and use the Commutative Property of Multiplication. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. The student will create equations to represent equivalent mathematical relationships. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Demonstrate fluency of multiplication facts with factors up to 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. B53: Multiplying by 8 Curriculum Standards: Use the Distributive Property and known facts to break apart unknown facts with 8 as a factor. Use strategies such as bar diagrams and arrays with known facts to solve multiplication problems. Use strategies such as skip counting and properties of operations to multiply. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Demonstrate fluency of multiplication facts with factors up to 10. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. Demonstrate fluency with products within 100. B54: Multiplying Three Numbers Curriculum Standards: Use the Associative Property of Multiplication to group 3 factors and multiply. Use properties of multiplication to find products when one factor is a multiple of 10. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Multiply whole numbers by multiples of 10 in the range 10- 90. B55: Meanings for Division Curriculum Standards: Use sharing to separate equal groups and to think about division. Use repeated subtraction to show the relationship between division and subtraction. Interpret whole- number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (e.g., describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real- world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret quotients of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. B56: Writing Division Stories Curriculum Standards: Use division to write and solve real-world problems involving equal groups. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Recognize the relationship between multiplication and division to represent and solve real-world problems. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Illustrate and explain using the relationship between multiplication and division. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Demonstrate fluency with products within 100. B57: Relating Multiplication and Division Curriculum Standards: Use multiplication facts to divide. Use patterns and known facts to find unknown multiplication facts. Use multiplication facts to find related division facts. Use multiplication and division facts to find unknown values in equations. Use a multiplication table to find the missing factor in a division problem. Use number sense and reasoning while practicing multiplication and division basic facts. Solve multiplication and division problems that involve different strategies and representations. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 =?). Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. The student will create equations to represent equivalent mathematical relationships. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division to represent and solve real-world problems. Demonstrate fluency of multiplication facts with factors up to 10. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Illustrate and explain using the relationship between multiplication and division. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Determine the unknown number in a multiplication or division equation relating three whole numbers. Demonstrate fluency with products within 100. B58: Dividing by 2 Through 5 Curriculum Standards: Use multiplication facts to find related division facts. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division to represent and solve real-world problems. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. B59: Dividing by 6 and 7 Curriculum Standards: Use multiplication facts to find related division facts. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division to represent and solve real-world problems. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. B60: Dividing by 8 and 9 Curriculum Standards: Use multiplication facts to find related division facts. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division to represent and solve real-world problems. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. B61: 0 and 1 in Division Curriculum Standards: Use properties to understand division involving 0 and 1. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division to represent and solve real-world problems. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. B62: Using Multiplication to Compare B63: Multiplication and Arrays B64: Breaking Apart Numbers to Multiply B65: Multiplying Two-Digit Numbers B66: Mental Math: Multiplication Patterns B67: Mental Math: Division Patterns B68: Estimating Products B69: Divisibility by 2, 3, 5, 9, and 10 Curriculum Standards: Use knowledge of even and odd numbers to identify multiplication patterns. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. B70: Divisibility Curriculum Standards: Use the multiplication table and the Distributive Property to find patterns in factors and products. Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real- world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Demonstrate fluency of multiplication facts with factors up to 10. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. Know from memory all products with factors up to and including 10. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Use multiplication and division within 100 to solve problems. Apply properties of operations as strategies to multiply and divide. Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. Demonstrate fluency with products within 100. Identify arithmetic patterns and explain the patterns using properties of operations. B71: Mental Math: Multiplying by Multiples of 10 B72: Mental Math: Using Properties B73: Using Mental Math to Multiply B74: Adding and Subtracting on a Number Line Curriculum Standards: Add and subtract on a number line. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2… and represent whole-number sums and differences within 100 on a number line diagram. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points and represent whole-number sums and differences, within 100, on a number line. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line. B75: Skip Counting on the Number Line Curriculum Standards: Use number lines to join equal groups. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Interpret the factors as representing the number of equal groups and the number of objects in each group. Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. Represent, interpret, and solve one-step problems involving multiplication and division. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Interpret products of whole numbers. Describe in words or drawings a problem that illustrates a multiplication or division situation. Use multiplication and division within 100 to solve problems. B76: Make 10 to Subtract Curriculum Standards: Make a 10 to subtract quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B77: More Make 10 to Subtract Curriculum Standards: Make a 10 to subtract quickly and accurately. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B78: Use Patterns to Develop Fluency in Addition Curriculum Standards: Use patterns to add numbers together. Fluently add and subtract within 5. The student will recognize and describe with fluency part-whole relationships for numbers up to 5. The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. Compose and decompose numbers up to 10 with objects and pictures. Recognize and combine groups with totals up to 5 (conceptual subitizing). Demonstrate fluency with addition and subtraction within 5. Recognize, without counting, the quantity of groups up to 5 objects arranged in common patterns. Demonstrate fluency for addition and subtraction within 5. B79: Count to Add on a Number Line Curriculum Standards: Count on and count back on a number line to subtract. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Count on to add using an open number line. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Count, with and without objects, forward and backward from any given number up to 120. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part- total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s. Use knowledge of number relationships to locate the position of a given whole number on an open number line up to 20. Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Counting on Using a number line Demonstrate fluency with addition and subtraction within 20. Add within 100. Use addition and subtraction within 20 to solve problems. B80: Count to Subtract on an Open Number Line Curriculum Standards: Count on and count back on a number line to subtract. Add and subtract quickly and accurately using mental math strategies. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate fluency with addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Use the relationship between addition and subtraction to generate basic facts up to 20. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Generate real-world situations to represent number sentences and vice versa. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Demonstrate fluency with addition and subtraction within 20. B81: Patterns on Multiplication Tables Booklet C: Computation with Whole numbers in Grades K-3 C1: Adding Tens Curriculum Standards: Add using place value and partial sums. Add numbers using partial sums. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add 2 multiples of 10. Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two- digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Find a number that is 10 more or 10 less than a given number. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. A two-digit number and a one-digit number A two-digit number and a multiple of 10 Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add within 100. C2: Adding on a Hundred Chart Curriculum Standards: Add within 100 using place-value strategies and a hundred chart. Choose and use any strategy to add two-digit numbers. Add using place value and partial sums. Add numbers using partial sums. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. C3: Adding Tens to a Two-Digit Number Curriculum Standards: Add using place value and partial sums. Add numbers using partial sums. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C4: Adding two-Digit Numbers Curriculum Standards: Use models to add 2-digit numbers and then explain the work. Add 2- digit numbers and then explain the work. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two- step practical problems involving addition and subtraction. Add numbers using partial sums. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two- digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C5: Estimating Sums C6: Regrouping in Addition Curriculum Standards: Use models to add 2-digit numbers and then explain the work. Add 2- digit numbers and then explain the work. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two- step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C7: Deciding When to Regroup in Addition Curriculum Standards: Use models to add 2-digit numbers and then explain the work. Add 2- digit numbers and then explain the work. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two- step practical problems involving addition and subtraction. Add 2 two-digit numbers. Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two- digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. The student, given a familiar problem situation involving magnitude, will select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, 500). The student will demonstrate an understanding of equality through the use of the equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. A two-digit number and a one-digit number A two-digit number and a multiple of 10 Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add within 100. C8: Adding Two-Digit and One-Digit Numbers Curriculum Standards: Use models to add 2-digit numbers and then explain the work. Add 2- digit numbers and then explain the work. Use mental math strategies and models to add more than two numbers. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. C9: Adding with Regrouping Curriculum Standards: Use models to add 2-digit numbers and then explain the work. Add 2- digit numbers and then explain the work. Use mental math strategies and models to add more than two numbers. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. C10: Two-Digit Addition Curriculum Standards: Add 2-digit numbers and then explain the work. Use mental math strategies and models to add more than two numbers. Model and solve two-step problems using equations. Use different ways to solve two-step problems. Add three or four 2-digit numbers. Add up to four two-digit numbers using strategies based on place value and properties of operations. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two- step practical problems involving addition and subtraction. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Make models to help solve math problems. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. Use models and equations to solve word problems. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Model with mathematics. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. Add or subtract within 1000, and justify the solution. Model with mathematics. C11: Adding Three Numbers Curriculum Standards: Use mental math strategies and models to add more than two numbers. Add three or four 2-digit numbers. Add up to four two-digit numbers using strategies based on place value and properties of operations. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Demonstrate fluency with addition and subtraction within 100. Add up to four two-digit numbers. Write and solve problems involving addition and subtraction within 100. C12: Subtracting Tens Curriculum Standards: Use a hundred chart to subtract a multiple of 10 from another multiple of 10. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count and explain the reasoning used. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences) using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. The student will demonstrate an understanding of equality through the use of the equal symbol. Find a number that is 10 more or 10 less than a given number. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Concrete models and drawings Strategies based on place value Properties of operations Calculate 10 more or 10 less than a given number mentally without having to count. Add or subtract a multiple of 10 from another two-digit number, and justify the solution. C13: Finding Parts of 100 C14: Subtracting on a Hundred Chart C15: Subtracting Tens from a Two-Digit Number C16: Subtracting Two-Digit Numbers Curriculum Standards: Use place value to subtract 2-digit numbers. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two- digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C17: Estimating Differences C18: Subtracting Two-Digit and One-Digit Numbers Curriculum Standards: Exchange 1 ten for 10 ones. Use place value and models to subtract 2- digit and 1-digit numbers. Use place value and regrouping to subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Model and solve two-step problems using equations. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use objects and number lines to represent number sentences. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real- world situations to represent number sentences and vice versa. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add or subtract within 1000, and justify the solution. C19: Deciding When to Regroup in Subtraction Curriculum Standards: Exchange 1 ten for 10 ones. Use place value and models to subtract 2- digit and 1-digit numbers. Use place value and regrouping to subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use objects and number lines to represent number sentences. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C20: Subtracting with Regrouping Curriculum Standards: Use place value and models to subtract 2-digit numbers. Use place value to subtract 2-digit numbers. Model problems using equations with unknowns in any position. Use drawings and equations to make sense of the words in problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. Exchange 1 ten for 10 ones. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Solve real- world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use objects and number lines to represent number sentences. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add or subtract within 1000, and justify the solution. C21: Two-Digit Subtraction Curriculum Standards: Use place value and models to subtract 2-digit numbers. Use place value to subtract 2-digit numbers. Use models and equations to solve word problems. Use drawings and equations to make sense of the words in problems. Model and solve two-step problems using equations. Use different ways to solve two-step problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two- digit numbers. Use objects and number lines to represent number sentences. Model problems using equations with unknowns in any position. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add or subtract within 1000, and justify the solution. C22: Using Addition to Check Subtraction Curriculum Standards: Add to check subtraction. Subtract 2-digit numbers and decide when to regroup and when not to regroup. Solve one-step and multi-step problems using strategies based on the relationship between addition and subtraction. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real- world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Use the relationship between addition and subtraction to solve problems. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 1000. C23: Adding on a Hundred Chart Curriculum Standards: Add within 100 using place-value strategies and a hundred chart. Choose and use any strategy to add two-digit numbers. Identify patterns in the addition table and explain them using algebraic thinking. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Use mental strategies and algorithms based on knowledge of place value to add and subtract two- digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Interpret patterns of multiplication on a hundreds board and/or multiplication table. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. Identify arithmetic patterns and explain the patterns using properties of operations. C24: Subtracting on a Hundred Chart Curriculum Standards: Use a hundred chart to subtract tens and ones. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will count backward by tens from 120. The student will determine sums and differences, using various methods. The student will create and solve single-step and two- step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C25: Using Mental Math to Add Curriculum Standards: Add within 100 using place-value strategies. Break apart numbers into tens and ones to find their sum. Break apart addends and combine them in different ways to make numbers that are easy to add mentally. Choose and use any strategy to add two-digit numbers. Use mental math to add. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. The student will create equations to represent equivalent mathematical relationships. Add 2-digit numbers and then explain the work. Use mental strategies and algorithms based on knowledge of place value to add and subtract two- digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Apply commutative and identity properties and number sense to find values for unknowns that make number sentences involving addition and subtraction true or false. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. Demonstrate fluency with addition and subtraction within 1000. C26: Using Mental Math to Subtract Curriculum Standards: Make numbers that are easier to subtract, and use mental math to find the difference. Solve one- and two-step problems using addition or subtraction. Use mental math to subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. The student will create equations to represent equivalent mathematical relationships. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 100. Use the relationship between addition and subtraction to solve problems. Write and solve problems involving addition and subtraction within 100. Add or subtract within 1000, and justify the solution. Demonstrate fluency with addition and subtraction within 1000. C27: Adding Two-Digit Numbers Curriculum Standards: Add two 3-digit numbers by breaking apart problems into simpler problems. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real- world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. C28: Subtracting Two-Digit Numbers Curriculum Standards: Subtract multi-digit numbers using the expanded algorithm. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real- world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. C29: Estimating Sums Curriculum Standards: Use rounding or compatible numbers to estimate a sum. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. The student will estimate and determine the sum or difference of two whole numbers. Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. C30: Estimating Differences Curriculum Standards: Use rounding or compatible numbers to estimate a difference. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. The student will estimate and determine the sum or difference of two whole numbers. Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. C31: Mental Math Strategies Curriculum Standards: Use mental math to subtract. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. The student will create equations to represent equivalent mathematical relationships. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. C32: Adding Three-Digit Numbers Curriculum Standards: Add 3-digit numbers using mental math strategies. Use different addition strategies and explain why they work. Add 3-digit numbers using the standard algorithm. Use an open number line to add 3-digit numbers. Use models to add 3-digit numbers. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real- world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Concrete models or drawings Strategies based on place value Properties of operations Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. Add or subtract mentally 10 or 100 to or from a given number within 1000. Understand that 100 can be thought of as 10 tens – called a “hundred”. Demonstrate fluency with addition and subtraction within 1000. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. C33: Subtracting Three-Digit Numbers Curriculum Standards: Use models to subtract 3-digit numbers. Subtract 3-digit numbers using the standard algorithm. Subtract a 3-digit number from another 3-digit number with one or more zeros by using the standard algorithm. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Concrete models or drawings Strategies based on place value Properties of operations Relationship between addition and subtraction Understand that 100 can be thought of as 10 tens – called a “hundred”. Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Demonstrate fluency with addition and subtraction within 1000. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. C34: Adding Three Numbers Curriculum Standards: Add three or more numbers using the standard algorithm. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. The student will estimate and determine the sum or difference of two whole numbers. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Add and subtract whole numbers up to and including 1,000. Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. Use expanded form to decompose numbers and then find sums and differences. Demonstrate fluency with addition and subtraction within 1000. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. C35: Subtracting Across Zero C36: Add with Tens on an Open Number Line Curriculum Standards: Add tens to two-digit numbers using an open number line. Choose and use any strategy to add two-digit numbers. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use objects and number lines to represent number sentences. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Count within 1000 by 1s, 10s and 100s starting with any number. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. C37: Add Two-Digit Numbers on an Open Number Line Curriculum Standards: Use an open number line to add tens and ones within 100. Choose and use any strategy to add two-digit numbers. Add up to subtract using an open number line. Add 3-digit numbers using mental math strategies. Use an open number line to add 3-digit numbers. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Add up to four two-digit numbers using strategies based on place value and properties of operations. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use a number line to solve addition problems. Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two- digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. The student, given a familiar problem situation involving magnitude, will select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, 500). The student will demonstrate an understanding of equality through the use of the equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use objects and number lines to represent number sentences. Find a number that is 10 more or 10 less than a given number. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Concrete models or drawings Strategies based on place value Properties of operations A two-digit number and a one-digit number A two-digit number and a multiple of 10 Count within 1000 by 1s, 10s and 100s starting with any number. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Add up to four two-digit numbers. Use the relationship between addition and subtraction to solve problems. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. Add or subtract mentally 10 or 100 to or from a given number within 1000. Add within 100. C38: Subtract Tens on an Open Number Line Curriculum Standards: Use an open number line to subtract tens. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will count backward by tens from 120. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Use objects and number lines to represent number sentences. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C39: Subtract Two-Digit Numbers on an Open Number Line Curriculum Standards: Use an open number line to subtract tens. Use an open number line to subtract tens and ones. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will count backward by tens from 120. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two- digit numbers. Use objects and number lines to represent number sentences. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. C40: Use Compensation to Add Curriculum Standards: Make numbers that are easier to subtract, and use mental math to find the difference. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Add 3-digit numbers using partial sums. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Concrete models or drawings Strategies based on place value Properties of operations Demonstrate fluency with addition and subtraction within 100. Use the relationship between addition and subtraction to solve problems. Write and solve problems involving addition and subtraction within 100. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. C41: Break Apart Numbers to Subtract Curriculum Standards: Break apart 1-digit numbers to make it easier to subtract mentally. Break apart 2-digit numbers to make it easier to subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Demonstrate fluency with addition and subtraction within 100. Use the relationship between addition and subtraction to solve problems. Write and solve problems involving addition and subtraction within 100. C42: Partial Sums Curriculum Standards: Add using place value and partial sums. Add numbers using partial sums. Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add 3-digit numbers using partial sums. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Selecting an appropriate strategy in order to efficiently compute sums and differences. Add up to three two-digit numbers using strategies based on place value and properties of operations. Concrete models or drawings Strategies based on place value Properties of operations Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. C43: Make 10 to Add 2-Digit Numbers Curriculum Standards: Solve addition problems by using blocks or drawings. Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two- digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. The student, given a familiar problem situation involving magnitude, will select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, 500). The student will demonstrate an understanding of equality through the use of the equal symbol. Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Find a number that is 10 more or 10 less than a given number. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. A two-digit number and a one-digit number A two-digit number and a multiple of 10 Add within 100. C44: Counting Up to Subtract on an Open Number Line Curriculum Standards: Use an open number line to add up to subtract 3-digit numbers. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Comparing addition and subtraction strategies, and explaining why they work. Concrete models or drawings Strategies based on place value Properties of operations Relationship between addition and subtraction Count within 1000 by 1s, 10s and 100s starting with any number. Add or subtract within 1000, and justify the solution. Use the relationship between addition and subtraction to solve problems. C45: Adding 10 and 100 to Numbers Curriculum Standards: Add 10 or 100 mentally using place value. Use an open number line to add 3-digit numbers. Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number 100-900. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. The student will determine sums and differences, using various methods. The student will create and solve single-step and two- step practical problems involving addition and subtraction. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Flexibly using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Concrete models or drawings Strategies based on place value Properties of operations Demonstrate fluency with addition and subtraction within 100. Add or subtract mentally 10 or 100 to or from a given number within 1000. Count within 1000 by 1s, 10s and 100s starting with any number. Read and write numbers to 1000 using number names, base-ten numerals and expanded form. Add or subtract within 1000, and justify the solution. C46: Subtracting 10 and 100 from Numbers Curriculum Standards: Subtract 10 or 100 mentally using place-value strategies. Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number 100-900. Explain why addition and subtraction strategies work, using place value and the properties of operations. Instructional Note: Explanations may be supported by drawing or objects. The student will identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999. Add 10 or 100 mentally using place value. Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Comparing addition and subtraction strategies, and explaining why they work. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Add or subtract within 1000, and justify the solution. Add or subtract mentally 10 or 100 to or from a given number within 1000. Demonstrate fluency with addition and subtraction within 100. C47: Use an Open Number Line to Multiply Curriculum Standards: Use an open number line to find products when one factor is a multiple of 10. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. Multiply whole numbers by multiples of 10 in the range 10-90. Booklet D: Measurement, Geometry, Data, and Probability in Grades K-3 D1: Time to the Hour Curriculum Standards: Tell time and use reasoning to state if the event is happening in the a.m. or p.m. Count within 1000 and skip-count by 5s, 10s and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. The student will tell time and write time to the nearest five minutes, using analog and digital clocks. Tell time to the hour. Tell and write time in hours and half-hours using analog and digital clocks. The student will investigate the passage of time and tell time to the hour and half-hour, using analog and digital clocks. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Tell time to the quarter-hour and distinguish between a.m. and p.m. Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. Tell time to the hour and half-hour. Tell time to the hour and half-hour (analog and digital). Count within 1000; skip-count by 5s, 10s, and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Tell and write time in hours and half-hours using analog and digital clocks. Count within 1000 by 1s, 10s and 100s starting with any number. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock. Tell and write time in hours and half-hours using analog and digital clocks. Demonstrate an understanding of concepts of time and devices that measure time. D2: Time to the Half Hour Curriculum Standards: Tell time and use reasoning to state if the event is happening in the a.m. or p.m. Count within 1000 and skip-count by 5s, 10s and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. The student will tell time and write time to the nearest five minutes, using analog and digital clocks. Tell time to the half hour. Tell and write time in hours and half-hours using analog and digital clocks. The student will investigate the passage of time and tell time to the hour and half-hour, using analog and digital clocks. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Tell time to the quarter- hour and distinguish between a.m. and p.m. Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. Tell time to the hour and half-hour. Tell time to the hour and half-hour (analog and digital). Count within 1000; skip-count by 5s, 10s, and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Tell and write time in hours and half-hours using analog and digital clocks. Count within 1000 by 1s, 10s and 100s starting with any number. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock. Tell and write time in hours and half- hours using analog and digital clocks. Demonstrate an understanding of concepts of time and devices that measure time. D3: Time to Five Minutes Curriculum Standards: Tell time to the nearest five minutes. Say the time in different ways. Tell time and use reasoning to state if the event is happening in the a.m. or p.m. Count within 1000 and skip- count by 5s, 10s and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. The student will tell time and write time to the nearest five minutes, using analog and digital clocks. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Tell time to the quarter-hour and distinguish between a.m. and p.m. Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. Count within 1000; skip-count by 5s, 10s, and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Count within 1000 by 1s, 10s and 100s starting with any number. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock. D4: Time Before and After the Hour Curriculum Standards: Say the time in different ways. Tell time and use reasoning to state if the event is happening in the a.m. or p.m. Count within 1000 and skip-count by 5s, 10s and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. The student will tell time and write time to the nearest five minutes, using analog and digital clocks. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Tell time to the quarter-hour and distinguish between a.m. and p.m. Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. Count within 1000; skip-count by 5s, 10s, and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Count within 1000 by 1s, 10s and 100s starting with any number. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock. D5: Time to the Quarter Hour Curriculum Standards: Say the time in different ways. Tell time and use reasoning to state if the event is happening in the a.m. or p.m. Count within 1000 and skip-count by 5s, 10s and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. The student will tell time and write time to the nearest five minutes, using analog and digital clocks. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Tell time to the quarter-hour and distinguish between a.m. and p.m. Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. Count within 1000; skip-count by 5s, 10s, and 100s. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Count within 1000 by 1s, 10s and 100s starting with any number. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock. D6: Telling Time Curriculum Standards: Show and tell time to the nearest minute using analog and digital clocks. Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). The student will tell time to the nearest minute, using analog and digital clocks. Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. Tell and write time to the nearest minute. Estimate time intervals in minutes. Solve problems involving addition and subtraction of minutes. D7: Units of Time D8: Elapsed Time Curriculum Standards: Tell and write time to the nearest minute and measure time intervals in minutes. Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). The student will solve practical problems related to elapsed time in one-hour increments within a 12-hour period. Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools. Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. Tell and write time to the nearest minute. Estimate time intervals in minutes. Solve problems involving addition and subtraction of minutes. D9: Comparing and Ordering by Length Curriculum Standards: Compare objects by length and height. Directly compare two objects with a measurable attribute in common, to see which object has “more of” or “less of” the attribute, and describe the difference. The student will compare two objects or events, using direct comparisons, according to one or more of the following attributes: length (longer, shorter), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder), volume (more, less), and time (longer, shorter). Order objects by length. Order three objects by length and compare the lengths of two objects indirectly by using a third object. The student will use nonstandard units to measure and compare length, weight, and volume. Measure the length of an object in terms of multiple copies of another object. Use nonstandard and standard measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement. Use words to compare objects according to length, size, weight and position. Order 2 or 3 objects using measurable attributes, such as length and weight. Use words to compare objects according to length, size, weight, position, and location. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. Order three objects by length; compare the lengths of two objects indirectly by using a third object. Order three or more objects by length. Compare the lengths of two objects indirectly by using a third object. Compare the measurable attributes of two objects. D10: Comparing and Ordering by Capacity D11: Comparing and Ordering by Weight D12: Unit Size and Measuring Curriculum Standards: Use objects to measure length. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Instructional Note: Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. The student will use nonstandard units to measure and compare length, weight, and volume. Estimate measures and use a ruler to measure length and height to the nearest centimeter. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Estimate lengths using units of inches, feet, centimeters, and meters. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. Measure the length of an object in terms of multiple copies of another object. Use nonstandard and standard measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement. Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other. Measure the same object/distance with units of two different lengths and describe how and why the measurements differ. Describe a length to the nearest whole unit using a number and a unit. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. Express the length of an object as a whole number of non-standard length units. Measure by laying multiple copies of a shorter object (the length unit) end to end (iterating) with no gaps or overlaps. Measure the length of an object by selecting and using appropriate tools. Estimate lengths using units of inches, feet, yards, centimeters and meters. Demonstrate the ability to measure length or distance using objects. D13: Inches and Feet Curriculum Standards: Estimate the length of an object by relating the length of the object to a measurement I know. Estimate measures and use a ruler to measure length and height to the nearest inch. Estimate measures and use tools to measure the length and height of objects to the nearest inch, foot, and yard. Estimate and measure the length and height of objects in inches, feet, and yards. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements, describe how the two measurements relate to the size of the unit chosen. The student will estimate and measure length to the nearest inch. Estimate lengths using units of inches, feet, centimeters, and meters. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. Estimate lengths using units of inches, feet, yards, centimeters and meters. Measure the length of an object by selecting and using appropriate tools. Analyze the results of measuring the same object with different units. D14: Centimeters Curriculum Standards: Estimate measures and use a ruler to measure length and height to the nearest centimeter. Estimate measures and use a ruler, meter stick, or tape measure to measure length and height to the nearest centimeter or meter. Measure the length and height of objects using different metric units. Tell how much longer one object is than another. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements, describe how the two measurements relate to the size of the unit chosen. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. Estimate lengths using units of inches, feet, centimeters, and meters. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. Measure the length of an object by selecting and using appropriate tools. Estimate lengths using units of inches, feet, yards, centimeters and meters. Analyze the results of measuring the same object with different units. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Measure to determine how much longer one object is than another. Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. D15: Inches, Feet, and Yards Curriculum Standards: Estimate the length of an object by relating the length of the object to a measurement I know. Estimate measures and use a ruler to measure length and height to the nearest inch. Estimate measures and use tools to measure the length and height of objects to the nearest inch, foot, and yard. Estimate and measure the length and height of objects in inches, feet, and yards. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements, describe how the two measurements relate to the size of the unit chosen. The student will estimate and measure length to the nearest inch. Estimate lengths using units of inches, feet, centimeters, and meters. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. Estimate lengths using units of inches, feet, yards, centimeters and meters. Measure the length of an object by selecting and using appropriate tools. Analyze the results of measuring the same object with different units. D16: Inches Curriculum Standards: Estimate measures and use a ruler to measure length and height to the nearest inch. Measure the lengths of objects and make a line plot to organize the data. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. The student will estimate and measure length to the nearest inch. Estimate lengths using units of inches, feet, centimeters, and meters. Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. Measure the length of an object by selecting and using appropriate tools. Estimate lengths using units of inches, feet, yards, centimeters and meters. Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers. Generate measurement data to the nearest whole unit, and display the data in a line plot. Solve problems using information presented in line plots, picture graphs and bar graphs. Draw conclusions from line plots, picture graphs and bar graphs. D17: Centimeters and Meters Curriculum Standards: Estimate measures and use a ruler, meter stick, or tape measure to measure length and height to the nearest centimeter or meter. Measure the length and height of objects using different metric units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements, describe how the two measurements relate to the size of the unit chosen. Estimate lengths using units of inches, feet, centimeters, and meters. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. Measure the length of an object by selecting and using appropriate tools. Estimate lengths using units of inches, feet, yards, centimeters and meters. Analyze the results of measuring the same object with different units. D18: Perimeter Curriculum Standards: Find the perimeter of different polygons. Find the perimeter of different polygons with common shapes. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. The student will estimate and measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units. Find the perimeter of a polygon by adding the lengths of the sides. Measure distances around objects. Find perimeter of polygon, given whole number lengths of the sides, in real-world and mathematical situations. Relate area to the operations of multiplication and addition. Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. Calculate area by using unit squares to cover a plane figure with no gaps or overlaps. Solve problems involving perimeters of polygons. D19: Exploring Area Curriculum Standards: Use unit squares to find the area of a shape. Use unit squares to find the area of a figure. Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area and can be used to measure area. Recognize area as an attribute of plane figures and understand concepts of area measurement. A plane figure which can be covered without gaps or overlaps by b unit squares is said to have an area of b square units. Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). The student will estimate and count the number of square units needed to cover a given surface in order to determine its area. Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. Calculate area by using unit squares to cover a plane figure with no gaps or overlaps. Label area measurements with squared units. D20: Finding Area on a Grid Curriculum Standards: Use unit squares to find the area of a shape. Use unit squares to find the area of a figure. Use standard units to measure the area of a shape. Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area and can be used to measure area. Recognize area as an attribute of plane figures and understand concepts of area measurement. A plane figure which can be covered without gaps or overlaps by b unit squares is said to have an area of b square units. Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). The student will estimate and count the number of square units needed to cover a given surface in order to determine its area. Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Calculate area by using unit squares to cover a plane figure with no gaps or overlaps. Label area measurements with squared units. D21: Area of Rectangles and Squares Curriculum Standards: Use unit squares and multiplication to find the areas of squares and rectangles. Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares. Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning. Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value. Multiply whole-number side lengths to solve problems involving the area of rectangles. D22: Area of Irregular Figures Curriculum Standards: Use areas of rectangles to find the area of irregular shapes. Relate area to the operations of multiplication and addition. Recognize area as additive and find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non- overlapping parts, applying this technique to solve real world problems. Find the area of two- dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. Decompose a rectangle into smaller rectangles to find the area of the original rectangle. D23: Rectangles with the Same Area or Perimeter Curriculum Standards: Understand the relationship of shapes with the same perimeter and different areas. Understand the relationship of shapes with the same area and different perimeters. Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Find the perimeter of a polygon by adding the lengths of the sides. Measure distances around objects. Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Relate area to the operations of multiplication and addition. Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. Solve problems involving perimeters of polygons. Understand that rectangles can have equal perimeters but different areas, or rectangles can have equal areas but different perimeters. D24: Using Customary Units of Capacity D25: Using Metric Units of Capacity Curriculum Standards: Use standard units to estimate liquid volume. Use pictures to help solve problems about mass and volume. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one- step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. Instructional Note: Exclude compound units such as cm3 and finding the geometric volume of a container. The student will estimate and use U.S. Customary and metric units to measure liquid volume in cups, pints, quarts, gallons, and liters. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Demonstrate fluency of multiplication facts with factors up to 10. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Solve problems involving customary measurement. Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds. Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units. Measure or estimate length, liquid volume and weight of objects. Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. D26: Using Metric Units of Mass Curriculum Standards: Use standard units to estimate the masses of solid objects. Use a pan balance with metric weights to measure the mass of objects in grams and kilograms. Use pictures to help solve problems about mass and volume. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. Instructional Note: Exclude compound units such as cm3 and finding the geometric volume of a container. The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. Demonstrate fluency of multiplication facts with factors up to 10. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. Solve problems involving customary measurement. Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds. Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units. Measure or estimate length, liquid volume and weight of objects. Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. D27: Using Customary Units of Weight D28: Position and Location Curriculum Standards: Describe positions of shapes in the environment. Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind and next to. The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space. Use basic shapes and spatial reasoning to model objects in the real-world. Use words to compare objects according to length, size, weight and position. Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably. Use basic shapes and spatial reasoning to represent objects in the real world. Use words to compare objects according to length, size, weight, position, and location. Describe objects in the environment using names of shapes, and describe the relative positions of objects using positional terms. Describe the relative positions of objects in space. D29: Shape Curriculum Standards: Build 2.D shapes that match given attributes. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes (e.g., having sides of equal length). Instructional Note: Student focus should include real-world shapes. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. The student will identify and describe plane figures (circle, triangle, square, and rectangle). Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. Use smaller shapes to form a larger shape when there is an outline to follow. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, attributes and other properties. Building and drawing triangles, rectangles, squares, hexagons, circles. Building cubes, cones, spheres, and cylinders. Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes Draw or model simple two-dimensional shapes. D30: Properties of Plane Shapes Curriculum Standards: Recognize shapes by how they look. Describe plane shapes by how they look. Draw polygon shapes. Analyze and compare 2.D shapes. Analyze and compare two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes (e.g., having sides of equal length). Instructional Note: Student focus should include real-world shapes. The student will identify and describe plane figures (circle, triangle, square, and rectangle). The student will compare the size (smaller, larger) and shape of plane figures (circle, triangle, square, and rectangle). The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space. Use attributes to match shapes. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, and/or overall size); build and draw shapes to possess defining attributes. The student will identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles. The student will identify and describe representations of circles, squares, rectangles, and triangles in different environments, regardless of orientation, and explain reasoning. The student will sort and classify concrete objects according to one or two attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. The student will identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms). Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. Recognize trapezoids and hexagons. Describe, compare, and classify two-dimensional figures according to their geometric attributes. Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. Identify trapezoids and hexagons by pointing to the shape when given the name. Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. Sort objects using characteristics such as shape, size, color and thickness. Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, attributes and other properties. Building and drawing triangles, rectangles, squares, trapezoids, hexagons, circles. Building cubes, rectangular prisms, cones, spheres, and cylinders. Recognize and draw triangles, quadrilaterals, pentagons, and hexagons, having specified attributes; recognize and describe attributes of rectangular prisms and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or sides. Identify triangles, quadrilaterals, pentagons, hexagons, circles and cubes. Distinguish between defining attributes versus non-defining attributes; build and draw shapes that possess defining attributes. Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes D31: Solid Figures Curriculum Standards: Name shapes as flat or solid. Through the use of real-life objects, identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). The student will identify and describe plane figures (circle, triangle, square, and rectangle). Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. Sort objects using characteristics such as shape, size, color and thickness. Recognize squares, circles, triangles, and rectangles. Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably. Use basic shapes and spatial reasoning to represent objects in the real world. Identify squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres as two-dimensional or three-dimensional. Identify shapes and describe objects in the environment using names of shapes, recognizing the name stays the same regardless of orientation or size. D32: Flat Surfaces of Solid Figures Curriculum Standards: Analyze and compare 2.D and 3.D shapes. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes (e.g., having sides of equal length). Instructional Note: Student focus should include real-world shapes. The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space. Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. Sort objects using characteristics such as shape, size, color and thickness. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, attributes and other properties. Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes D33: Making New Shapes from Shapes Curriculum Standards: Use materials to build 3.D shapes. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Compose simple shapes to form larger shapes (e.g., “Can these two triangles, with full sides touching, join to make a rectangle?”). The student will identify and describe plane figures (circle, triangle, square, and rectangle). Combine 2-D shapes to make another 2-D shape. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape and compose new shapes from the composite shape. Instructional Note: Students do not need to learn formal names such as, “right rectangular prism.” The student will identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles. The student will sort and classify concrete objects according to one or two attributes. Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. Compose and decompose larger shapes using smaller two-dimensional shapes. Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. Compose free- form shapes with blocks. Building and drawing triangles, rectangles, squares, hexagons, circles. Building cubes, cones, spheres, and cylinders. Compose larger shapes from simple shapes. Making a two- dimensional composite shape using rectangles, squares, trapezoids, triangles, and half-circles naming the components of the new shape. Making a three-dimensional composite shape using cubes, rectangular prisms, cones, and cylinders, naming the components of the new shape. Compose and decompose two- and three-dimensional shapes to build an understanding of part-whole relationships and the properties of the original and composite shapes. Draw or model simple two-dimensional shapes. Compose simple shapes to form larger shapes using manipulatives. D34: Cutting Shapes Apart D35: Flat Surfaces and Corners D36: Faces, Corners, and Edges Curriculum Standards: Draw cubes and describe how they look. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. The student will identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms). Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. Describe, compare, and classify two-dimensional figures according to their geometric attributes. Recognize and draw triangles, quadrilaterals, pentagons, and hexagons, having specified attributes; recognize and describe attributes of rectangular prisms and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or sides. Identify triangles, quadrilaterals, pentagons, hexagons, circles and cubes. Identify the faces of three- dimensional objects. D37: Solid Figures Curriculum Standards: Draw cubes and describe how they look. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. The student will identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms). Define 3-D shapes by their number of edges, vertices, and faces or flat surfaces. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, and/or overall size); build and draw shapes to possess defining attributes. The student will sort and classify concrete objects according to one or two attributes. Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. Describe, compare, and classify two-dimensional figures according to their geometric attributes. Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. Compose and decompose larger shapes using smaller two-dimensional shapes. Recognize and draw triangles, quadrilaterals, pentagons, and hexagons, having specified attributes; recognize and describe attributes of rectangular prisms and cubes. Building and drawing triangles, rectangles, squares, trapezoids, hexagons, circles. Building cubes, rectangular prisms, cones, spheres, and cylinders. Recognize and draw shapes having specified attributes, such as a given number of angles or sides. Identify triangles, quadrilaterals, pentagons, hexagons, circles and cubes. Identify the faces of three-dimensional objects. Distinguish between defining attributes versus non-defining attributes; build and draw shapes that possess defining attributes. D38: Lines and Line Segments D39: Acute, Right, and Obtuse Angles D40: Polygons Curriculum Standards: Describe plane shapes by how they look. Draw polygon shapes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. The student will identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms). Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. Recognize trapezoids and hexagons. Describe, compare, and classify two-dimensional figures according to their geometric attributes. Recognize and draw triangles, quadrilaterals, pentagons, and hexagons, having specified attributes; recognize and describe attributes of rectangular prisms and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or sides. Identify triangles, quadrilaterals, pentagons, hexagons, circles and cubes. D41: Classifying Triangles Using Sides and Angles D42: Quadrilaterals Curriculum Standards: Identify quadrilaterals and use attributes to describe them. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. Reason with two-dimensional shapes and their attributes. Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids. Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. D43: Graphing D44: Sorting and Classifying Curriculum Standards: Classify objects into categories and tell why they are in each category. Classify objects into given categories, count the numbers of objects in each category, and sort the categories by count. Category counts should be limited to less than or equal to 10. (e.g., Identify coins and sort them into groups of 5s or 10s.) The student will sort and classify objects according to one attribute. Sort objects using characteristics such as shape, size, color and thickness. Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common. Collect and sort information about objects and events in the environment. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Compare two numerals, between 1 and 10, and determine which is more than or less than the other. Classify objects into given categories; count the number of objects in each category. D45: Reading Picture Graphs Curriculum Standards: Draw picture graphs and use them to solve problems. Draw conclusions for graphs. Use graphs to compare and interpret data. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will read and interpret data represented in pictographs and bar graphs. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. The student will collect, organize, and represent data in pictographs and bar graphs. The student will read and interpret data represented in pictographs and bar graphs. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Interpret organized data. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Organize, represent, interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category and how many more or less are in one category than in another. The student, given up to 110 objects, will order three or fewer sets from least to greatest and greatest to least. The student will collect, organize, and represent various forms of data using tables, picture graphs, and object graphs. The student will read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category. Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s. Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one. Draw conclusions and make predictions from information in a graph. Use counting and comparison skills to create and analyze bar graphs and tally charts. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams). Use data to create picture and bar-type graphs to demonstrate one- to-one correspondence. Draw conclusions from picture and bar-type graphs. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two-step “how many more” and “how many less” problems using information from these graphs. Organize, represent, and interpret data with up to four categories. Draw a picture graph and a bar graph with a single-unit scale to represent a data set. Solve simple put-together, take-apart, and compare problems using information presented in a picture and a bar graph. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare- Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Add to/Take from-Change Unknown Put together/Take Apart-Addend Unknown Compare-Difference Unknown Organize, represent, and interpret data with up to three categories. Ask and answer questions about the total number of data points. Ask and answer questions about how many in each category. Ask and answer questions about how many more or less are in one category than in another. Draw a picture graph or a bar graph to represent a data set with up to four categories. Solve problems using information presented in line plots, picture graphs and bar graphs. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Draw conclusions from line plots, picture graphs and bar graphs. Use multiplication and division within 100 to solve problems. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. Use addition and subtraction within 20 to solve problems. Collect, organize and represent data with up to three categories. Draw conclusions from object graphs, picture graphs, T-charts and tallies. D46: Interpreting Graphs Curriculum Standards: Draw bar graphs and use them to solve problems. Use graphs to solve problems. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. The student will collect, organize, and represent data in pictographs and bar graphs. The student will read and interpret data represented in pictographs and bar graphs. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will read and interpret data represented in pictographs and bar graphs. Draw conclusions for graphs. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category. Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one. Draw conclusions and make predictions from information in a graph. Organize, represent, and interpret data with up to four categories. Draw a picture graph and a bar graph with a single-unit scale to represent a data set. Solve simple put-together, take-apart, and compare problems using information presented in a picture and a bar graph. Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. Use estimation strategies to assess reasonableness of answers. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two-step “how many more” and “how many less” problems using information from these graphs. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Draw a picture graph or a bar graph to represent a data set with up to four categories. Solve problems using information presented in line plots, picture graphs and bar graphs. Use multiplication and division within 100 to solve problems. Write and solve two-step problems involving variables using any of the four operations. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Draw conclusions from line plots, picture graphs and bar graphs. D47: Reading Bar Graphs Curriculum Standards: Use graphs to compare and interpret data. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will read and interpret data represented in pictographs and bar graphs. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two- step “how many more” and “how many less” problems using information from these graphs. Use multiplication and division within 100 to solve problems. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. D48: Tallying Results Curriculum Standards: Count how many objects are in different categories. Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. Classify objects into given categories, count the numbers of objects in each category, and sort the categories by count. Category counts should be limited to less than or equal to 10. (e.g., Identify coins and sort them into groups of 5s or 10s.) The student will collect, organize, and represent data. The student will sort and classify objects according to one attribute. Organize data into categories. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Organize, represent, interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category and how many more or less are in one category than in another. The student, given up to 110 objects, will order three or fewer sets from least to greatest and greatest to least. The student will collect, organize, and represent various forms of data using tables, picture graphs, and object graphs. The student will read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to. Use counting and comparison skills to create and analyze bar graphs and tally charts. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams). Use data to create picture and bar-type graphs to demonstrate one-to- one correspondence. Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Sort objects using characteristics such as shape, size, color and thickness. Recognize that a number can be used to represent how many objects are in a set up to 10. Count forward, with and without objects, from any given number up to 10. Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives. Collect and sort information about objects and events in the environment. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. Given a number from 1– 20, count out that many objects. Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. Given 10 objects in a scattered arrangement, identify how many. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Add to/Take from-Change Unknown Put together/Take Apart-Addend Unknown Compare-Difference Unknown Organize, represent, and interpret data with up to three categories. Ask and answer questions about the total number of data points. Ask and answer questions about how many in each category. Ask and answer questions about how many more or less are in one category than in another. Use addition and subtraction within 20 to solve problems. Collect, organize and represent data with up to three categories. Draw conclusions from object graphs, picture graphs, T-charts and tallies. Count forward beginning from a given number between 1 and 20. Read and write numerals and represent a number of objects from 0 to 20. Demonstrate that a number can be used to represent “how many” are in a set. Compare two numerals, between 1 and 10, and determine which is more than or less than the other. Classify objects into given categories; count the number of objects in each category. D49: Real Graphs D50: Data and Picture Graphs Curriculum Standards: Use frequency tables and picture graphs to compare and interpret data. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will collect, organize, and represent data in pictographs or bar graphs. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two-step “how many more” and “how many less” problems using information from these graphs. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. D51: Making Bar Graphs Curriculum Standards: Draw bar graphs and use them to solve problems. Use frequency tables and picture graphs to compare and interpret data. Draw a picture graph and a bar graph (with single- unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. The student will collect, organize, and represent data in pictographs and bar graphs. The student will read and interpret data represented in pictographs and bar graphs. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will collect, organize, and represent data in pictographs or bar graphs. Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category. Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Organize, represent, and interpret data with up to four categories. Draw a picture graph and a bar graph with a single-unit scale to represent a data set. Solve simple put-together, take-apart, and compare problems using information presented in a picture and a bar graph. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two- step “how many more” and “how many less” problems using information from these graphs. Draw a picture graph or a bar graph to represent a data set with up to four categories. Solve problems using information presented in line plots, picture graphs and bar graphs. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. D52: Make a Graph D53: Recording Data from a Survey D54: Making Line Plots Curriculum Standards: Measure the lengths of objects and make a line plot to organize the data. Measure length to the nearest fourth inch and show the data on a line plot. Measure length to the nearest half inch and show the data on a line plot. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. The student will estimate and measure length to the nearest inch. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves or quarters. The student will name and write fractions and mixed numbers represented by a model. The student will represent fractions and mixed numbers with models and symbols. The student will estimate and use U.S. Customary and metric units to measure length to the nearest ½ inch, inch, foot, yard, centimeter, and meter. Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. Use half units when measuring distances. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Estimate and measure lengths in customary units to the quarter-inch and half-inch, and feet and yards to the whole unit. Measure the length of an object by selecting and using appropriate tools. Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers. Generate measurement data to the nearest whole unit, and display the data in a line plot. Solve problems using information presented in line plots, picture graphs and bar graphs. Draw conclusions from line plots, picture graphs and bar graphs. Create a line plot to represent data. Use data shown in a line plot to answer questions. D55: Reading and Making Pictographs Curriculum Standards: Draw picture graphs and use them to solve problems. Draw conclusions for graphs. Use scaled bar graphs to represent data sets. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will collect, organize, and represent data in pictographs or bar graphs. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems using information presented in a bar graph. The student will collect, organize, and represent data in pictographs and bar graphs. The student will read and interpret data represented in pictographs and bar graphs. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Interpret organized data. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Organize, represent, interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category and how many more or less are in one category than in another. The student, given up to 110 objects, will order three or fewer sets from least to greatest and greatest to least. The student will collect, organize, and represent various forms of data using tables, picture graphs, and object graphs. The student will read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category. Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s. Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one. Draw conclusions and make predictions from information in a graph. Use counting and comparison skills to create and analyze bar graphs and tally charts. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams). Use data to create picture and bar-type graphs to demonstrate one- to-one correspondence. Draw conclusions from picture and bar-type graphs. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two-step “how many more” and “how many less” problems using information from these graphs. Organize, represent, and interpret data with up to four categories. Draw a picture graph and a bar graph with a single-unit scale to represent a data set. Solve simple put-together, take-apart, and compare problems using information presented in a picture and a bar graph. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare- Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Add to/Take from-Change Unknown Put together/Take Apart-Addend Unknown Compare-Difference Unknown Organize, represent, and interpret data with up to three categories. Ask and answer questions about the total number of data points. Ask and answer questions about how many in each category. Ask and answer questions about how many more or less are in one category than in another. Draw a picture graph or a bar graph to represent a data set with up to four categories. Solve problems using information presented in line plots, picture graphs and bar graphs. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Draw conclusions from line plots, picture graphs and bar graphs. Use multiplication and division within 100 to solve problems. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. Use addition and subtraction within 20 to solve problems. Collect, organize and represent data with up to three categories. Draw conclusions from object graphs, picture graphs, T-charts and tallies. D56: Reading and Making a Bar Graph Curriculum Standards: Use scaled bar graphs to represent data sets. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). The student will collect, organize, and represent data in pictographs or bar graphs. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. Represent and interpret scaled picture and bar graphs: Collect data by asking a question that yields data in up to four categories. Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. Solve one and two- step “how many more” and “how many less” problems using information from these graphs. Use multiplication and division within 100 to solve problems. Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. Solve one- and two-step problems using information presented in bar and/or picture graphs. D57: More Perimeter D58: Measuring Capacity or Weight D59: Solving Problems with Units of Time Curriculum Standards: Solve word problems involving addition and subtraction to measure quantities of time. Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). The student will solve practical problems related to elapsed time in one-hour increments within a 12-hour period. Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. Know relationships among units of time. Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools. Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. Tell and write time to the nearest minute. Estimate time intervals in minutes. Solve problems involving addition and subtraction of minutes. D60: Comparing by Length Curriculum Standards: Use the given sides of a polygon and the known perimeter to find the unknown side length. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Find the perimeter of a polygon by adding the lengths of the sides. Measure distances around objects. Relate area to the operations of multiplication and addition. Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. Solve problems involving perimeters of polygons. D61: Comparing by Capacity D62: Comparing by Weight D63: Indirect Measurement D64: Compose with 3-D Shapes D65: Add and Subtract with Measurements Curriculum Standards: Tell how much longer one object is than another. Solve problems by adding or subtracting length measurements. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Measure to determine how much longer one object is than another. Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. D66: Find Unknown Measurements Curriculum Standards: Tell how much longer one object is than another. Solve problems by adding or subtracting length measurements. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Add or subtract to solve problems about measurements. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Measure to determine how much longer one object is than another. Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. Demonstrate fluency with addition and subtraction within 20. Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line. D67: Divide Rectangles into Equal Shares Curriculum Standards: Add or subtract to solve problems about measurements. Add and subtract to solve measurement problems by using drawings and equations. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Divide rectangles into equal squares. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line. Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares. D68: Equal Shares, Different Shapes Curriculum Standards: Divide rectangles into equal squares. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Use repeated reasoning to divide rectangles into rows and columns and to create designs with equal shares. The student will represent fractional parts with models and with symbols. Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Look for and express regularity in repeated reasoning. Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares. Look for and express regularity in repeated reasoning. D69: Area and the Distributive Property Curriculum Standards: Make equal shares that do not have the same shape. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. The student will name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths. The student will represent fractional parts with models and with symbols. Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, fourths, fourth of, quarter of. Describe the whole as two halves, three thirds, four fourths. Explain that equal shares of identical wholes need not have the same shape. Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole. Demonstrate that equal shares of identical wholes need not have the same shape. D70: Perimeter and Unknown Side Lengths Curriculum Standards: Use areas of rectangles to model the Distributive Property of Multiplication. Relate area to the operations of multiplication and addition. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Relate area to the operations of multiplication and addition. Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles, and that the area of the large rectangle is the sum of the two smaller rectangles. Find rectangular arrangements that can be formed for a given area. Booklet E: Problem Solving in Grades K-3 E1: Analyze Given Information Curriculum Standards: Solve one- and two-step problems using addition or subtraction. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. One-Step problems: Add to/Take from- Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Demonstrate fluency with addition and subtraction within 100. Add or subtract within 1000, and justify the solution. Write and solve problems involving addition and subtraction within 100. E2: Two-Step Problems Curriculum Standards: Use drawings and equations to solve one-step and two-step problems. Use drawings, models, and equations to solve one- and two-step problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single- step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. Use models and equations to solve word problems. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. Add or subtract within 1000, and justify the solution. E3: Multi-Step Problems Curriculum Standards: Use drawings and equations to solve one-step and two-step problems. Use drawings, models, and equations to solve one- and two-step problems. Model and solve two-step problems using equations. Use different ways to solve two-step problems. Draw diagrams and write equations to solve two-step problems involving addition and subtraction of whole numbers. Solve two- step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. Use estimation strategies to assess reasonableness of answers. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Demonstrate fluency with addition and subtraction within 20. Add or subtract within 1000, and justify the solution. Write and solve two-step problems involving variables using any of the four operations. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. E4: Use Data from a Table or Chart E5: Analyze Given Information E6: Two-Step Problems Curriculum Standards: Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer. Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. Use estimation strategies to assess reasonableness of answers. Write and solve two-step problems involving variables using any of the four operations. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. E7: Multi-Step Problems Curriculum Standards: Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer. Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. Use estimation strategies to assess reasonableness of answers. Write and solve two-step problems involving variables using any of the four operations. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. E8: Look for a Pattern E9: Look for a Pattern E10: Make a Table and Look for a Pattern E11: Draw a Picture E12: Make a Table E13: Use Tools E14: Act It Out E15: Make an Organized List E16: Try, Check, and Revise E17: Use Reasoning Curriculum Standards: Use attributes to describe different objects. Describe measurable attributes of objects, such as length or weight and describe several measurable attributes of a single object. The student will compare two objects or events, using direct comparisons, according to one or more of the following attributes: length (longer, shorter), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder), volume (more, less), and time (longer, shorter). Use words to compare objects according to length, size, weight and position. Order 2 or 3 objects using measurable attributes, such as length and weight. Use words to compare objects according to length, size, weight, position, and location. Describe measurable attributes of objects; and describe several different measurable attributes of a single object. Describe several measureable attributes of objects. E18: Use Reasoning E19: Draw a Picture and Write a Number Sentence Curriculum Standards: Make arrays with equal rows or equal columns to solve addition problems. Use number patterns on an addition facts table to complete related addition equations that show basic facts. Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. The student will determine sums and differences, using various methods. The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtration to generate basic facts. Demonstrate fluency with basic addition facts and related subtraction facts. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Demonstrate fluency with basic addition facts and related subtraction facts up to 20. Use concrete models and structured arrangements, such as repeated addition, arrays and ten frames to develop understanding of multiplication. Use objects and number lines to represent number sentences. Solve word problems involving comparisons. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). The student will create and solve single-step story and picture problems using addition and subtraction within 20. The student will demonstrate an understanding of equality through the use of the equal symbol. Use words, pictures, objects, length- based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Add and subtract on a number line. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2… and represent whole-number sums and differences within 100 on a number line diagram. The student will create and solve single-step and two-step practical problems involving addition and subtraction. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real- world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Demonstrate fluency with addition and subtraction, within 20, using mental strategies. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Add to/Take from-Change Unknown Put together/Take Apart-Addend Unknown Compare-Difference Unknown Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points and represent whole-number sums and differences, within 100, on a number line. Demonstrate fluency with addition and subtraction within 20. Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. Demonstrate fluency with addition and subtraction within 100. Write and solve problems involving addition and subtraction within 100. Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line. Use addition and subtraction within 20 to solve problems. E20: Draw a Picture and Write a Number Sentence E21: Make a Table and Look for a Pattern E22: Act It Out E23: Make an Organized List E24: Try, Check, and Revise E25: Draw a Strip Diagram and Write a Number Sentence Curriculum Standards: Use drawings, models, and equations to solve one- and two-step problems. Use models and equations to solve word problems. Model problems using equations with unknowns in any position. Model and solve two-step problems using equations. Use different ways to solve two-step problems. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Two-Step problems involving single digits: Add to/Take from- Change Unknown Add to/Take from- Change Unknown Demonstrate fluency with addition and subtraction within 100. Add or subtract within 1000, and justify the solution. Write and solve problems involving addition and subtraction within 100. E26: Use Tools Curriculum Standards: Choose an appropriate tool and use it to measure a given object. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Instructional Note: Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. The student will use nonstandard units to measure and compare length, weight, and volume. Measure the length of an object in terms of multiple copies of another object. Use nonstandard and standard measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement. Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other. Describe a length to the nearest whole unit using a number and a unit. Use appropriate tools strategically. Use appropriate tools strategically. E27: Draw a Strip Diagram E28: Use Representations E29: Use Representations E30: Work Backward E31: Make and Test Generalizations Curriculum Standards: Classify shapes according to their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. Reason with two-dimensional shapes and their attributes. Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids. Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. E32: Make and Test Generalizations Curriculum Standards: Analyze and compare quadrilaterals and group them by their attributes. Recognize area as an attribute of plane figures and understand concepts of area measurement. A plane figure which can be covered without gaps or overlaps by b unit squares is said to have an area of b square units. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. Reason with two-dimensional shapes and their attributes. Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids. Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. E33: Writing to Explain E34: Writing to Explain Curriculum Standards: Critique the reasoning of others by using known information about addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Apply properties of operations as strategies to add and subtract (e.g., If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known: Commutative Property of Addition. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12: Associative Property of Addition). Instructional Note: Students need not use formal terms for these properties. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 and use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8= 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). The student will create and solve single-step story and picture problems using addition and subtraction within 20. Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. E35: Writing Math Stories E36: Writing Math Stories E37: Use Data from a Table or Chart E38: Work Backward E39: Draw a Picture E40: Make a Table E41: Analyze Given Information E42: Draw a Picture and Write a Number Sentence Curriculum Standards: Model problems using equations with unknowns in any position. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). The student will determine sums and differences, using various methods. The student will create and solve single-step and two-step practical problems involving addition and subtraction. The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. Generate real-world situations to represent number sentences and vice versa. One-Step problems: Add to/Take from-Start Unknown Compare-Bigger Unknown Compare-Smaller Unknown Demonstrate fluency with addition and subtraction within 100. Add or subtract within 1000, and justify the solution. Write and solve problems involving addition and subtraction within 100. E43: Draw a Strip Diagram and Write an Equation E44: Use Representations E45: Solve a Simpler Problem E46: Use Reasoning E47: Analyze Relationships E48: Make and Test Conjectures E49: Reasonableness E50: Represent Subtraction as Taking Apart E51: Solve 2-Step Word Problems: Multiplication and Division Curriculum Standards: Draw diagrams and write equations to solve two-step problems involving multiplication and division of whole numbers. Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. Use estimation strategies to assess reasonableness of answers. Write and solve two-step problems involving variables using any of the four operations. Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. Diagnostic Tests and Answer Keys, Grades K-3 N70: Stem-and-Leaf Plots Grade K Diagnostic Test, Form A Grade K Diagnostic Test, Form B Grade 1 Diagnostic Test, Form A Grade 1 Diagnostic Test, Form B Grade 2 Diagnostic Test, Form A Grade 2 Diagnostic Test, Form B Grade 3 Diagnostic Test, Form A Grade 3 Diagnostic Test, Form B Booklet F: Numeration, Patterns, and Relationships in Grades 4-6 F1: Ways to Show Numbers F2: Numbers to 999 on the Number Line F3: Skip Counting on the Number Line F4: Rounding to the Nearest Ten and Hundred F5: Reading and Writing 4-Digit Numbers F6: Numbers Halfway Between and Rounding F7: Comparing and Ordering Numbers F8: Place-Value Patterns F9: Place Value Through Thousands Curriculum Standards: Read and write numbers in expanded form, with numerals, and using number names. Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. F10: Rounding Numbers Through Thousands Curriculum Standards: Use place value to round multi-digit numbers. Use place value understanding to round multi-digit whole numbers to any place. The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Round multi-digit whole numbers to any place. F11: Comparing and Ordering Numbers Through Thousands Curriculum Standards: Use place value to compare multi-digit numbers. Read and write multi- digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi- digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order whole numbers expressed through millions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. F12: Place Value Through Millions Curriculum Standards: Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Explain the patterns in the place value system from one million to the thousandths place. Explain that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. Understand that in a multi- digit number, a digit represents 1/10 times what it would represents in the place to its left. F13: Rounding Numbers Through Millions F14: Comparing and Ordering Numbers Through Millions F15: Place Value Through Billions F16: Place Value Through Trillions F17: Exponents and Place Value Curriculum Standards: Use exponents to write powers of 10 and calculate products. Use place- value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Evaluate the value of powers of 10 and understand the relationship to the place value system. F18: Meaning of Integers F19: Comparing and Ordering Integers F20: Comparing and Ordering Rational Numbers F21: Adding Integers F22: Subtracting Integers F23: Multiplying and Dividing Integers F24: Repeating Patterns Curriculum Standards: Generate a shape pattern that follows a given rule and predict a shape in the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create growth patterns involving geometric shapes and define the single operation rule of the pattern. Generate and analyze a number or shape pattern that follows a given rule. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. F25: Number Patterns Curriculum Standards: Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. Analyze numerical patterns. Use tables to identify relationships between patterns. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. (e.g., Given the rule “Add 3” and the starting number 0 and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.) Represent real-world mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems. Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates. Generate and analyze a number or shape pattern that follows a given rule. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns. Graph the ordered pairs on a coordinate plane. Make and interpret a representation of data using a line graph. Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Generate two numeric patterns given two rules. Identify the relationship between two numeric patterns. Write a rule to describe or explain a given numeric pattern. Investigate the relationship between two numeric patterns. Translate two numeric patterns into two sets of ordered pairs. Graph numeric patterns on the Cartesian coordinate plane. Plot and interpret points in the first quadrant of the Cartesian coordinate plane. F26: Input/Output Tables Curriculum Standards: Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. Analyze numerical patterns. Use tables to identify relationships between patterns. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. (e.g., Given the rule “Add 3” and the starting number 0 and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.) Represent real-world mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Create an input/output chart or table to represent or extend a numerical pattern. Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real- world and mathematical problems. Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates. Generate and analyze a number or shape pattern that follows a given rule. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns. Graph the ordered pairs on a coordinate plane. Make and interpret a representation of data using a line graph. Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. Generate a number pattern that follows a given rule. Use words or mathematical symbols to express a rule for a given pattern. Generate two numeric patterns given two rules. Identify the relationship between two numeric patterns. Write a rule to describe or explain a given numeric pattern. Investigate the relationship between two numeric patterns. Translate two numeric patterns into two sets of ordered pairs. Graph numeric patterns on the Cartesian coordinate plane. Plot and interpret points in the first quadrant of the Cartesian coordinate plane. F27: Geometric Growth Patterns F28: Expressions with Addition and Subtraction F29: Expressions with Multiplication and Division F30: Find a Rule F31: Patterns and Equations F32: Graphing Ordered Pairs Curriculum Standards: Locate points on a coordinate grid. Graph points on a coordinate grid. Solve real-world problems by graphing points. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines, the origin, arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real-world mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate expressions and solve equations involving variables when values for the variables are given. Create and analyze line and double-bar graphs with whole numbers, fractions, and decimals increments. Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems. Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates. Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. Make and interpret a representation of data using a line graph. Define a first quadrant Cartesian coordinate system. Represent the axes as scaled perpendicular number lines that both intersect at 0, the origin. Identify any point on the Cartesian coordinate plane by its ordered pair coordinates. Define the first number in an ordered pair as the horizontal distance from the origin. Define the second number in an ordered pair as the vertical distance from the origin. Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. Plot and interpret points in the first quadrant of the Cartesian coordinate plane. F33: Lengths of Line Segments F34: Graphing Equations F35: Graphing Points in the Coordinate Plane F36: Graphing Equations in the Coordinate Plane F37: Translating Words to Expressions F38: Equality and Inequality Curriculum Standards: Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.) Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate expressions and solve equations involving variables when values for the variables are given. Solve real- world and mathematical problems requiring addition, subtraction, multiplication, and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: Translate written expressions into algebraic expressions. F39: Multiplication Properties F40: Expressions with Parentheses Curriculum Standards: Use the order of operations to evaluate expressions. Evaluate expressions with parentheses, brackets, and braces. Write simple expressions that show calculations with numbers. Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols. The student will simplify whole number numerical expressions using the order of operations. Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.) Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate expressions and solve equations involving variables when values for the variables are given. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: Parentheses, using the order of operations. Commutative, associative and distributive properties. Write, evaluate and interpret numeric expressions using the order of operations. Translate written expressions into algebraic expressions. F41: Order of Operations Curriculum Standards: Use the order of operations to evaluate expressions. Evaluate expressions with parentheses, brackets, and braces. Write simple expressions that show calculations with numbers. Interpret numerical expressions without evaluating them. Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols. The student will simplify whole number numerical expressions using the order of operations. Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.) Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate expressions and solve equations involving variables when values for the variables are given. Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: Parentheses, using the order of operations. Commutative, associative and distributive properties. Write, evaluate and interpret numeric expressions using the order of operations. Translate written expressions into algebraic expressions. F42: Using the Distributive Property Curriculum Standards: Use the Distributive Property to multiply larger numbers. Use place value and properties of operations to multiply mentally. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. F43: Properties of Operations F44: Variables and Expressions F45: More Variables and Expressions F46: Writing Expressions Curriculum Standards: Interpret comparisons as multiplication or addition equations. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. F47: Formulas and Equations F48: Properties of Equality F49: Solving Addition and Subtraction Equations F50: Solving Multiplication and Division Equations F51: Solving Equations with Whole Numbers F52: Solving Equations with Decimals F53: Writing Addition and Subtraction Equations F54: Writing Multiplication and Division Equations F55: Solving Equations with Fractions F56: Solving Equations with More Than One Operation F57: Perfect Squares F58: Identify Parts of Expressions F59: Write Equivalent Expressions F60: Simplify Algebraic Expressions F61: Write Inequalities F62: Solve Inequalities F63: Dependent and Independent Variables F64: Absolute Value Booklet G: Operations with Whole Numbers in Grades 4-6 G1: Addition Properties G2: Relating Addition and Subtraction G3: Using Mental Math to Add Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. G4: Using Mental Math to Subtract Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. G5: Estimating Sums Curriculum Standards: Round greater whole numbers to estimate sums and differences. Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi- digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi- digit whole number, a digit represent 10 times what it would represents in the place to its right. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G6: Estimating Differences Curriculum Standards: Round greater whole numbers to estimate sums and differences. Recognize the relationship between adjacent digits in a multi-digit number. Recognize that in a multi- digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will read, write, and identify the place and value of each digit in a nine-digit whole number. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. Understand that in a multi- digit whole number, a digit represent 10 times what it would represents in the place to its right. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G7: Adding Two-Digit Numbers G8: Subtracting Two-Digit Numbers G9: Mental Math Strategies Curriculum Standards: Add and subtract whole numbers mentally using a variety of methods. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. G10: Adding Three-Digit Numbers G11: Subtracting Three-Digit Numbers G12: Adding and Subtracting Money G13: Estimating Sums and Differences of Greater Numbers G14: Adding Three Numbers G15: Subtracting Four-Digit Numbers G16: Subtracting Across Zero Curriculum Standards: Use number sense and regrouping to subtract across zeros. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single- step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. G17: Adding 4-Digit Numbers G18: Adding Greater Numbers Curriculum Standards: Add numbers to one million with and without regrouping using the standard algorithm. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi- step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G19: Subtracting Greater Numbers Curriculum Standards: Use place value and an algorithm to subtract whole numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fluently add and subtract multi-digit whole numbers using the standard algorithm. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. Demonstrate fluency with addition and subtraction of whole numbers. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G20: Multiplication as Repeated Addition G21: Arrays and Multiplication G22: Using Multiplication to Compare Curriculum Standards: Interpret comparisons as multiplication or addition equations. Use multiplication and division to compare two quantities. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Find whole- number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. G23: Writing Multiplication Stories G24: Multiplying by 2 and 5 G25: Multiplying by 9 G26: Multiplying by 1 or 0 G27: Multiplying by 3 G28: Multiplying by 4 G29: Multiplying by 6 or 7 G30: Multiplying by 8 G31: Multiplying by 10 G32: Multiplying Three Numbers G33: Meanings for Division G34: Writing Division Stories G35: Relating Multiplication and Division G36: Dividing by 2 Through 5 G37: Dividing by 6 and 7 G38: Dividing by 8 and 9 G39: 0 and 1 in Division G40: Mental Math: Multiplication Patterns Curriculum Standards: Multiply multiples of 10, 100, and 1,000 using mental math and place- value strategies Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. G41: Mental Math: Division Patterns Curriculum Standards: Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole- number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. G42: Estimating Products Curriculum Standards: Use rounding to estimate products and check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G43: Estimating Quotients Curriculum Standards: Use compatible numbers to estimate quotients. Use place-value patterns and division facts to estimate quotients for 4-digit dividends. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Find whole-number quotients and remainders with up to three- digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. G44: Multiplication and Arrays G45: Breaking Apart Numbers to Multiply Curriculum Standards: Use arrays and partial products to multiply 3- and 4-digit numbers by 1- digit numbers. Use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G46: Multiplying Two-Digit Numbers Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G47: Multiplying Three-Digit Numbers Curriculum Standards: Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G48: Multiplying Money G49: Multiplying One-Digit and Four-Digit Numbers Curriculum Standards: Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G50: Dividing with Objects G51: Interpret the Remainder Curriculum Standards: Solve division problems and interpret remainders. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Interpret remainders in word problems. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. G52: Using Objects to Divide Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G53: Dividing Two-Digit Numbers Curriculum Standards: Use partial quotients to divide. Use partial quotients and place-value understandings to divide with greater dividends. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two- step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G54: Dividing Three-Digit Numbers Curriculum Standards: Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. Use partial quotients to divide. Use partial quotients and place-value understandings to divide with greater dividends. Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G55: Zeros in the Quotient G56: Dividing Greater Numbers Curriculum Standards: Use partial quotients to divide. Use partial quotients and place-value understandings to divide with greater dividends. Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine quotients of whole numbers, with and without remainders. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Interpret remainders in word problems. Represent problems using equations with a letter standing for the unknown quantity. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Solve multi- step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G57: Factoring Numbers Curriculum Standards: Use arrays to find the factors of a given whole number. Use multiplication to find all the factor pairs for a whole number. Use factors to determine whether a whole number greater than 1 is prime or composite. Find all factor pairs for a whole number in the range 1– 100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. G58: Divisibility by 2, 3, 5, 9, and 10 G59: Divisibility G60: Exponents G61: Prime Factorization G62: Greatest Common Factor G63: Least Common Multiple Curriculum Standards: Use multiplication to find multiples of a given number. Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number. Determine if the number is prime or composite. Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. G64: Mental Math: Multiplying by Multiples of 10 Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G65: Estimating Products Curriculum Standards: Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. Use compatible numbers to estimate products of 2-digit by 2- digit multiplication problems. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. Solve multi-step word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. G66: Using Arrays to Multiply Two-Digit Factors Curriculum Standards: Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one- digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G67: Multiplying Two-Digit Numbers by Multiples of 10 Curriculum Standards: Use models and properties of operations to multiply 2-digit numbers by multiples of ten. Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Multiply 3- digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. G68: Multiplying by Two-Digit Numbers Curriculum Standards: Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Use models and algorithms to solve 2-digit by 2-digit multiplication problems. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. The student will investigate and describe the concept of variable. The student will write an equation to represent a given mathematical relationship, using a variable. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. G69: Multiplying Greater Numbers Curriculum Standards: Multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. The student will write an equation to represent a given mathematical relationship, using a variable. The student will investigate and describe the concept of variable. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. G70: Mental Math: Using Properties Curriculum Standards: Use the Distributive Property and an area model to multiply two 2-digit numbers. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two- digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will estimate and determine sums, differences, and products of whole numbers. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi- digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. G71: Dividing by Multiples of 10 Curriculum Standards: Use place-value patterns and mental math to find quotients. Find the quotient when the divisor is a multiple of 10. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Solve real- world and mathematical problems requiring addition, subtraction, multiplication, and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Divide multi- digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. G72: Estimating Quotients with Two-Digit Divisors Curriculum Standards: Use compatible numbers and place-value patterns to estimate quotients. Decide where to place the first digit of the quotient when dividing whole numbers. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Estimate solutions to division problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Round numbers from billions to thousandths place. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four- digit dividends, and justify the solution. G73: Dividing by Two-Digit Divisors Curriculum Standards: Use models to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Solve real- world and mathematical problems requiring addition, subtraction, multiplication, and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. G74: One- and Two-Digit Quotients Curriculum Standards: Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Solve real- world and mathematical problems requiring addition, subtraction, multiplication, and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. G75: Dividing Greater Numbers Curriculum Standards: Use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. G76: Using Mental Math to Multiply Curriculum Standards: Use place value and properties of operations to multiply mentally. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Multiply 3-digit by 1- digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two- digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. G77: Adding and Subtracting on a Number Line G78: Skip Counting on the Number Line Booklet H: Fractions, Decimals, and Percents in Grades 4-6 H1: Equal Parts of a Whole H2: Parts of a Region H3: Fractions of a Set H4: Parts of a Set H5: Fractions and Length H6: Fractions on the Number Line H7: Working with Unit Fractions H8: Using Models to Compare Fractions H9: Using Models to Find Equivalent Fractions H10: Comparing Fractions on the Number Line H11: Comparing Fractions Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. H12: Fractions and Decimals Curriculum Standards: Relate fractions and decimals with denominators of 10 to 100. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will read, write, represent, and identify decimals expressed through thousandths. The student will given a model, write the decimal and fraction equivalents. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. H13: Counting Money Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. H14: Making Change Curriculum Standards: Use fractions or decimals to solve word problems involving money. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will add and subtract with decimals. The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. Solve word problems involving multiplication of a fraction by a whole number. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. H15: Using Money to Understand Decimals H16: Equivalent Fractions Curriculum Standards: Use area models to recognize and generate equivalent fractions. Use a number line to locate and identify equivalent fractions. Use multiplication to find equivalent fractions. Use division to find equivalent fractions. Find common denominators for fractions with unlike denominators. Represent data using line plots and interpret data in line plots to solve problems. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. The student will represent equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Explain and/or illustrate why two fractions are equivalent. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. H17: Fractions and Division H18: Estimating Fractional Amounts H19: Simplest Form H20: Mixed Numbers H21: Comparing and Ordering Fractions Curriculum Standards: Use benchmarks, area models, and number lines to compare fractions. Use models or rename fractions to compare. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. The student will represent equivalent fractions. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use benchmark fractions (0, ¼, ?, ½, ?, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: Reasoning about their size and using area and length models. Using benchmark fractions 0, ½, and a whole. Comparing common numerator or common denominators. Recognize and generate equivalent fractions. Compare two fractions using the symbols >, = or <, and justify the solution. H22: Comparing and Ordering Mixed Numbers H23: Fractions and Mixed Numbers on the Number Line H24: Place Value Through Hundredths H25: Decimals on the Number Line Curriculum Standards: Locate and describe fractions and decimals on number lines. Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). The student will given a model, write the decimal and fraction equivalents. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Represent tenths and hundredths with concrete models, making connections between fractions and decimals. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. Use decimal notation to represent fractions. Express, model and explain the equivalence between fractions with denominators of 10 and 100. Represent tenths and hundredths with models, making connections between fractions and decimals. Use decimal notation for fractions with denominators of 10 or 100. Understand that fractions and decimals are equivalent representations of the same quantity. Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. Understand that parts of a whole can be expressed as fractions and or decimals. Convert decimals to fractions and fractions to decimals. H26: Place Value Through Thousandths Curriculum Standards: Represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals. Read and write decimals through thousandths in different ways. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names and expanded form (e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)). The student will represent and identify equivalencies among fractions and decimals, with and without models. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. Explain the patterns in the place value system from one million to the thousandths place. Explain that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read, write, and compare decimals to thousandths. Write decimals using base-ten numerals, number names, and expanded form. Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left. Convert decimals to fractions and fractions to decimals. H27: Place Value Through Millionths H28: Rounding Decimals Through Hundredths H29: Rounding Decimals Through Thousandths Curriculum Standards: Round decimals to different places. Use place value understanding to round decimals to any place. The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth. Round numbers to the nearest 0.1, 0.01 and 0.001. Round numbers from billions to thousandths place. H30: Comparing and Ordering Decimals Through Hundredths Curriculum Standards: Compare decimals by reasoning about their size. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will compare and order decimals. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. Compare benchmark fractions (¼, ?, ½, ?, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. H31: Comparing and Ordering Decimals Through Thousandths Curriculum Standards: Use place value to compare decimals through thousandths. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. Compare and order fractions and or decimals to the thousandths place using the symbols >, = or <, and justify the solution. H32: Relating Fractions and Decimals Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H33: Decimals to Fractions H34: Fractions to Decimals Curriculum Standards: Add fractions with denominators of 10 and 100 by using equivalent fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use equivalent fractions to add two fractions with denominators of 10 or 100. Recognize and generate equivalent fractions. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H35: Relating Fractions and Decimals to Thousandths H36: Using Models to Compare Fractions and Decimals H37: Fractions, Decimals, and the Number Line Curriculum Standards: Estimate sums and differences of fractions by using the nearest half or whole number. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Estimate results of sums, differences and products with fractions and decimals to the thousandths. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. H38: Adding Fractions with Like Denominators Curriculum Standards: Decompose a fraction or mixed number into a sum of fractions in more than one way. Solve problems involving joining parts of the same whole by adding fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H39: Subtracting Fractions with Like Denominators Curriculum Standards: Use tools such as fraction strips, area models, and number lines to subtract fractions. Solve problems involving separating parts of the same whole by subtracting fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H40: Adding and Subtracting Fractions with Like Denominators H41: Adding and Subtracting Fractions on a Number Line Curriculum Standards: Count forward or backward on a number line to add or subtract. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. H42: Adding Fractions with Unlike Denominators Curriculum Standards: Estimate sums and differences of fractions by using the nearest half or whole number. Add fractions with unlike denominators using equivalent fractions with a common denominator. Subtract fractions with unlike denominators. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Estimate results of sums, differences and products with fractions and decimals to the thousandths. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. H43: Subtracting Fractions with Unlike Denominators Curriculum Standards: Estimate sums and differences of fractions by using the nearest half or whole number. Add fractions with unlike denominators using equivalent fractions with a common denominator. Subtract fractions with unlike denominators. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Estimate results of sums, differences and products with fractions and decimals to the thousandths. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. H44: Estimating Sums and Differences of Mixed Numbers Curriculum Standards: Estimate sums and differences of fractions and mixed numbers. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Estimate results of sums, differences and products with fractions and decimals to the thousandths. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi- step problems involving variables, whole numbers, fractions and decimals. H45: Adding Mixed Numbers Curriculum Standards: Solve problems using data in a line plot. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally). The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. Represent and interpret data. Collect data by asking a question that yields data that changes over time. Make and interpret a representation of data using a line graph. Determine whether a survey question will yield categorical or numerical data, or data that changes over time. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. H46: Subtracting Mixed Numbers Curriculum Standards: Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Solve and justify multi- step problems involving variables, whole numbers, fractions and decimals. H47: Multiplying Fractions by Whole Numbers Curriculum Standards: Use a model to understand a fraction as a multiple of a unit fraction. Use models to multiply fractions by whole numbers. Use symbols and equations to multiply a fraction by a whole number. Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. Multiply a whole number by a fraction. Multiply a fraction by a whole number. Multiply fractions and whole numbers. Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. (e.g., Use a visual fraction model to show (2/3) × 4 = 8/3 and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Use fraction models to add and subtract fractions with like denominators in real- world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. H48: Multiplying Two Fractions Curriculum Standards: Use models to multiply two fractions. Multiply two fractions. Find the area of a rectangle using fractions and diagrams. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. (e.g., Use a visual fraction model to show (2/3) × 4 = 8/3 and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find are areas of rectangles and represent fraction products as rectangular areas. Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. Use area and length models to multiply two fractions, with the denominators 2, 3, 4. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Calculate and interpret the product of two fractions less than one. Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. Justify the reasonableness of a product when multiplying with fractions. Estimate the size of the product based on the size of the two factors. Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1. H49: Understanding Division with Fractions Curriculum Standards: Understand how fractions are related to division. Implement division of fractions to show quotients as fractions and mixed numbers. Use multiplication to divide a whole number by a unit fraction. Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. Use models to divide unit fractions by non-zero whole numbers. Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Solve multi- step problems involving division with unit fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. (e.g., Interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. (e.g., Create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a whole number by a unit fraction and compute such quotients. (e.g., Create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. (e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many1/3-cup servings are in 2 cups of raisins?) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Use fractions to model and solve division problems. Interpret a fraction as an equal sharing context, where a quantity is divided into equal parts. Model and interpret a fraction as the division of the numerator by the denominator. Solve one-step word problems involving division of whole numbers leading to answers in the form of fractions and mixed numbers, with denominators of 2, 3, 4, 5, 6, 8, 10, and 12, using area, length, and set models or equations. Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. Calculate and interpret the quotient of a unit fraction by a non-zero whole number. Calculate and interpret the quotient of a whole number by a unit fraction. H50: Dividing Fractions H51: Estimating Products and Quotients of Mixed Numbers H52: Multiplying Mixed Numbers Curriculum Standards: Use models, equations, and previously learned strategies to multiply mixed numbers. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Solve problems using data in a line plot. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally). The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real- world and mathematical problems including those involving money, measurement, geometry, and data. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. Represent and interpret data. Collect data by asking a question that yields data that changes over time. Make and interpret a representation of data using a line graph. Determine whether a survey question will yield categorical or numerical data, or data that changes over time. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. Justify the reasonableness of a product when multiplying with fractions. Estimate the size of the product based on the size of the two factors. Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1. Calculate and interpret the product of two fractions less than one. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. H53: Dividing Mixed Numbers Curriculum Standards: Understand how fractions are related to division. Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. (e.g., Interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?) Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Use fractions to model and solve division problems. Interpret a fraction as an equal sharing context, where a quantity is divided into equal parts. Model and interpret a fraction as the division of the numerator by the denominator. Solve one- step word problems involving division of whole numbers leading to answers in the form of fractions and mixed numbers, with denominators of 2, 3, 4, 5, 6, 8, 10, and 12, using area, length, and set models or equations. H54: Using Models to Add and Subtract Decimals Curriculum Standards: Model sums and differences of decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. H55: Estimating Decimal Sums and Differences Curriculum Standards: Use rounding or compatible numbers to estimate sums and differences. Read and write whole numbers using standard form, expanded form, and number names. Use place value understanding to round decimals to any place. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single- step practical problems involving division of decimals. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Explain the patterns in the place value system from one million to the thousandths place. Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left. Round numbers from billions to thousandths place. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. H56: Adding Decimals to Hundredths Curriculum Standards: Use properties of addition and strategies to solve problems mentally. Add decimals to the hundredths using the standard algorithm. Subtract decimals to the hundredths using the standard algorithm. Add and subtract decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single- step practical problems involving division of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). Compute and solve real-world problems with multi- digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. H57: Subtracting Decimals to Hundredths Curriculum Standards: Use properties of addition and strategies to solve problems mentally. Add decimals to the hundredths using the standard algorithm. Subtract decimals to the hundredths using the standard algorithm. Add and subtract decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single- step practical problems involving division of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). Compute and solve real-world problems with multi- digit whole numbers and decimal numbers. Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. H58: More Estimation of Decimal Sums and Differences H59: Adding and Subtracting Decimals to Thousandths H60: Multiplying with Decimals and Whole Numbers Curriculum Standards: Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Evaluate the value of powers of 10 and understand the relationship to the place value system. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. H61: Multiplying Decimals by 10, 100, or 1,000 Curriculum Standards: Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Evaluate the value of powers of 10 and understand the relationship to the place value system. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. H62: Estimating the Product of a Whole Number and a Decimal Curriculum Standards: Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Evaluate the value of powers of 10 and understand the relationship to the place value system. Round numbers from billions to thousandths place. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. H63: Multiplying Decimals Using Grids Curriculum Standards: Use models to represent multiplying a decimal and a whole number. Use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole number. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. H64: Multiplying Decimals by Decimals Curriculum Standards: Use grids to model decimals and find the product of a decimal and a decimal. Multiply decimals using partial products and models. Use properties to multiply decimals. Use number sense and reasoning to place the decimal point in a product. Multiply decimals using the standard algorithm for multiplication and multiplication strategies. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Use estimation strategies to assess reasonableness of answers. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. H65: Dividing with Decimals and Whole Numbers H66: Dividing Decimals by 10, 100, or 1,000 Curriculum Standards: Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. Evaluate the value of powers of 10 and understand the relationship to the place value system. H67: Dividing a Decimal by a Whole Number Curriculum Standards: Use models to help find quotients in problems involving decimals. Use the standard algorithm for division to divide decimals by a whole number. Use models to visualize the relationship between division and multiplication to divide decimals by a 2-digit whole number. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. Use estimation strategies to assess reasonableness of answers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Divide multi- digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. H68: Estimating the Quotient of a Decimal and a Whole Number Curriculum Standards: Use reason and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single- step practical problems involving division of decimals. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. Use estimation strategies to assess reasonableness of answers. Round numbers from billions to thousandths place. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. H69: Dividing a Decimal by a Decimal Curriculum Standards: Use number sense and reasoning to place the decimal point in the quotient when dividing two decimals. Use the standard algorithm and place-value patterns to divide a decimal by another decimal. Use the standard algorithm to divide decimals, annexing zeros as needed. Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. The student will estimate and determine the product and quotient of two numbers involving decimals. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. Use estimation strategies to assess reasonableness of answers. Divide multi-digit whole numbers and decimals to the hundredths place using up to two- digit divisors and four-digit dividends, and justify the solution. H70: Understanding Ratios H71: Rates and Unit Rates H72: Comparing Rates H73: Distance, Rate, and Time H74: Equal Ratios and Proportions H75: Solving Proportions H76: Maps and Scale Drawings H77: Understanding Percent H78: Relating Percents, Decimals, and Fractions H79: Percents Greater Than 100 or Less Than 1 H80: Estimating Percent of a Number H81: Finding the Percent of a Whole Number H82: Tips and Sales Tax H83: Equivalent Fractions and the Number Line H84: Counting Coins and Bills H85: Estimating Fraction Sums and Differences Curriculum Standards: Use number lines and benchmark fractions to estimate fraction sums and differences. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. The student will add and subtract fractions and mixed numbers having like and unlike denominators. The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. H86: Divide Whole Numbers by Unit Fractions H87: Divide Unit Fractions by Non-Zero Whole Numbers H88: Find the Whole Booklet I: Measurement, Geometry, Data, and Probability in Grades 4-6 I1: Solid Figures I2: Lines and Line Segments Curriculum Standards: Draw and identify perpendicular, parallel, and intersecting lines. Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. The student will identify and describe intersecting, parallel, and perpendicular lines. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. I3: Acute, Right, and Obtuse Angles Curriculum Standards: Recognize and draw lines, rays, and angles with different measures. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Identify and estimate angles and their measure. I4: Polygons I5: Classifying Triangles Using Sides and Angles Curriculum Standards: Classify triangles by line segments and angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category (e.g., all rectangles have four right angles and squares are rectangles, so all squares have four right angles). Classify two-dimensional figures in a hierarchy based on properties. The student will classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Understand that attributes belonging to a category of figures also belong to all subcategories. Classify figures in a hierarchy based on properties. I6: Quadrilaterals Curriculum Standards: Classify quadrilaterals by lines and angles. Classify quadrilaterals by their properties. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category (e.g., all rectangles have four right angles and squares are rectangles, so all squares have four right angles). Classify two- dimensional figures in a hierarchy based on properties. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. Classify quadrilaterals into categories based on their properties. Explain that attributes belonging to a category of quadrilaterals also belong to all subcategories of that category. Classify quadrilaterals in a hierarchy based on properties. Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. Classify two-dimensional shapes by their sides and/or angles. Understand that attributes belonging to a category of figures also belong to all subcategories. Classify figures in a hierarchy based on properties. I7: Making New Shapes from Shapes I8: Cutting Shapes Apart I9: Congruent Figures and Motions I10: Line Symmetry Curriculum Standards: Recognize and draw lines of symmetry. Identify line symmetric figures. Draw figures that have line symmetry. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line- symmetric figures and draw lines of symmetry. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Recognize symmetry in a two- dimensional figure, and identify and draw lines of symmetry. Construct lines of symmetry for a two- dimensional figure. I11: Solids and Nets I12: Views of Solid Figures I13: Geometric Ideas I14: Congruent Figures I15: Circles I16: Rotational Symmetry I17: Transformations Curriculum Standards: Solve problems involving line plots and fractions. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. I18: Measuring and Classifying Angles Curriculum Standards: Find the measure of an angle that turns through a fraction of a circle. Use known angle measures to measure unknown angles. Use a protractor to measure and draw angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Develop an understanding of angles and angle measurement. Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. Measure and sketch angles in whole-number degrees using a protractor. Identify and estimate angles and their measure. Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. Draw and measure angles in whole-number degrees using a protractor. I19: Angle Pairs Curriculum Standards: Use addition and subtraction to solve problems with unknown angle measures. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Compare angles according to size. Classify angles as acute, right and obtuse. Develop an understanding of angles and angle measurement. Solve addition and subtraction problems to find unknown angles on a diagram in real- world and mathematical problems. I20: Missing Angles in Triangles and Quadrilaterals I21: Measuring Length to 1/2 and 1/4 Inch I22: Using Customary Units of Length Curriculum Standards: Convert customary units of length. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between inches, feet, and yards to measure and compare objects. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Convert measurements of capacity, length and weight within a given measurement system. Solve multi- step problems that require measurement conversions. I23: Using Metric Units of Length Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Convert metric units of length. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Evaluate the value of powers of 10 and understand the relationship to the place value system. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. I24: Using Customary Units of Capacity Curriculum Standards: Convert customary units of capacity. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Convert measurements of capacity, length and weight within a given measurement system. Solve multi- step problems that require measurement conversions. I25: Using Metric Units of Capacity Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Convert metric units of capacity. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Evaluate the value of powers of 10 and understand the relationship to the place value system. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. I26: Using Customary Units of Weight Curriculum Standards: Convert Customary Units of weight. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. I27: Using Metric Units of Mass Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Convert metric units of mass. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Evaluate the value of powers of 10 and understand the relationship to the place value system. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. I28: Time to the Quarter Hour I29: Telling Time I30: Units of Time Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I31: Elapsed Time Curriculum Standards: Use the four operations to solve problems involving time. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Solve problems involving the conversion of one measure of time to another. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve word problems involving addition and subtraction of time intervals that cross the hour. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. I32: Converting Customary Units of Length Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Convert customary units of length. Solve real-world problems with measurement conversions. Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between inches, feet, and yards to measure and compare objects. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Demonstrate fluency with the multiplication of two whole numbers up to a three- digit number by a two-digit number using the standard algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two- digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. I33: Converting Customary Units of Capacity Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Convert customary units of capacity. Solve real-world problems with measurement conversions. Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between inches, feet, and yards to measure and compare objects. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Demonstrate fluency with the multiplication of two whole numbers up to a three- digit number by a two-digit number using the standard algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two- digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. I34: Converting Customary Units of Weight Curriculum Standards: Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. Convert Customary Units of weight. Solve real-world problems with measurement conversions. Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between inches, feet, and yards to measure and compare objects. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Demonstrate fluency with the multiplication of two whole numbers up to a three- digit number by a two-digit number using the standard algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two- digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Solve problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. I35: Converting Metric Units Curriculum Standards: Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. Convert metric units of length. Convert metric units of capacity. Convert metric units of mass. Solve real-world problems with measurement conversions. Fluently multiply multi- digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between inches, feet, and yards to measure and compare objects. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. Demonstrate fluency with the multiplication of two whole numbers up to a three- digit number by a two-digit number using the standard algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. Solve word problems involving multiplication of a fraction by a whole number. Know relative sizes of measurement units. Solve problems involving metric measurement. Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. Know relative sizes of measurement units within one system of units. Convert measurements in a larger unit in terms of a smaller unit. Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. Evaluate the value of powers of 10 and understand the relationship to the place value system. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. I36: Converting Between Measurement Systems I37: Units of Measure and Precision I38: More Units of Time I39: More Elapsed Time I40: Elapsed Time in Other Units I41: Perimeter I42: Exploring Area I43: Finding Area on a Grid I44: More Perimeter Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. I45: Area of Rectangles and Squares Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. I46: Area of Irregular Figures I47: Rectangles with the Same Area or Perimeter Curriculum Standards: Find the unknown length or width of a rectangle using the known area or perimeter. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Solve word problems involving multiplication of a fraction by a whole number. Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. Solve problems with area and perimeter. Find areas of rectilinear figures with known side lengths. Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply the area and perimeter formulas for rectangles to solve problems. I48: Area of Parallelograms I49: Area of Triangles I50: Circumference I51: Area of a Circle I52: Surface Area of Rectangular Prisms I53: Surface Area I54: Counting Cubes to Find Volume Curriculum Standards: Find the volume of solid figures. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. Understand the concept of volume and recognize that volume is measured in cubic units. Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. Analyze and describe the properties of prisms and pyramids. I55: Measuring Volume Curriculum Standards: Find the volume of prisms in different ways. Find the volume of rectangular prisms using a formula. Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes (e.g., to represent the associative property of multiplication). Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems. The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. Relate volume to the operations of multiplication and addition. Find the volume of a rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths. Build understanding of the volume formula for rectangular prisms with whole-number edge lengths in the context of solving problems. Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. Understand the concept of volume and recognize that volume is measured in cubic units. Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. Apply the formulas V = l × w × h and V = B × h for volume of right rectangular prisms with whole-number edge lengths. I56: Comparing Volume and Surface Area I57: Recording Data from a Survey I58: Reading and Making Pictographs I59: Reading and Making a Bar Graph I60: Making Line Plots Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. I61: Interpreting Graphs I62: Stem-and-Leaf Plots I63: Histograms I64: Finding the Mean I65: Median, Mode, and Range I66: Scatterplots I67: Measuring Capacity or Weight I68: Solving Problems with Units of Time I69: Making Dot Plots Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. I70: Converting Units I71: Line Plots Curriculum Standards: Read and interpret data using line plots. Represent data using line plots and interpret data in line plots to solve problems. Solve problems involving line plots and fractions. Read and analyze line plots. Organize and display data in a line plot. Solve problems using data in a line plot. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally). The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. The student, given a practical problem, will represent data in line plots and stem-and-leaf plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data. Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. Represent and interpret data. Collect data by asking a question that yields data that changes over time. Make and interpret a representation of data using a line graph. Determine whether a survey question will yield categorical or numerical data, or data that changes over time. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Solve problems involving multiplication of a fraction by a whole number. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. Recognize and generate equivalent fractions. Create a frequency table and/or line plot to display measurement data. Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. Extend the concept of multiplication to multiply a fraction or whole number by a fraction. Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. I72: Combining Volumes Curriculum Standards: Find the volume of a solid figure that is the combination of two or more rectangular prisms. Use models, prior knowledge of volumes, and previously learned strategies to solve word problems involving volume. Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Recognize volume as additive and find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems. The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. Relate volume to the operations of multiplication and addition. Find volume of solid figures with one-digit dimensions composed of two non-overlapping rectangular prisms. Apply the formulas V = l × w × h and V = B × h for volume of right rectangular prisms with whole-number edge lengths. I73: Polygons on the Coordinate Plane I74: Statistical Questions I75: Box Plots I76: Measures of Variability I77: Appropriate Use of Statistical Measures I78: Summarize Data Distributions Booklet J: Problem Solving in Grades 4-6 J1: Analyze Given Information Curriculum Standards: Solve real-world problems with measurement conversions. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. The student will solve practical problems involving length, mass, and liquid volume using metric units. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Recognize and use the relationship between inches, feet, and yards to measure and compare objects. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. Convert measurements of capacity, length and weight within a given measurement system. Solve multi-step problems that require measurement conversions. J2: Two-Step Problems Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. J3: Multi-Step Problems Curriculum Standards: Solve multi-step problems by finding and solving hidden questions first. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two- digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four- digit dividends and one-digit divisors, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. J4: Two-Step Problems Curriculum Standards: Solve two-step problems by finding and solving the hidden question first. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will recognize and demonstrate the meaning of equality in an equation. Solve multi-step real- world and mathematical problems requiring the use of addition, subtraction and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. Multiply or divide to solve problems involving a multiplicative comparison. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. J5: Multi-Step Problems J6: Make an Organized List J7: Make an Organized List J8: Analyze Given Information J9: Draw a Picture and Write a Number Sentence Curriculum Standards: Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. The student will estimate and determine sums, differences, and products of whole numbers. The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. Use an understanding of place value to multiply a number by 10, 100 and 1000. Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. Solve two-step word problems involving the four operations with whole numbers. Use estimation strategies to assess reasonableness of answers. Represent problems using equations with a letter standing for the unknown quantity. Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. J10: Draw a Picture and Write a Number Sentence J11: Draw a Strip Diagram and Write an Equation J12: Draw a Strip Diagram and Write an Equation J13: Try, Check, and Revise J14: Try, Check, and Revise J15: Solve a Simpler Problem J16: Use Representations J17: Make a Table and Look for a Pattern J18: Solve a Simpler Problem J19: Make a Table and Look for a Pattern J20: Analyze Relationships J21: Use Objects J22: Use Objects J23: Use Reasoning J24: Use Reasoning J25: Draw a Picture J26: Draw a Picture J27: Work Backward J28: Work Backward J29: Make a Graph J30: Make a Graph J31: Analyze Relationships J32: Make and Test Generalizations J33: Make and Test Conjectures J34: Reasonableness J35: Reasonableness J36: Use Representations J37: Writing to Explain Curriculum Standards: Represent data using line plots and interpret data in line plots to solve problems. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Represent and interpret data using whole numbers. Collect data by asking a question that yields numerical data. Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. Determine whether a survey question will yield categorical or numerical data. Recognize and generate equivalent fractions. Solve problems involving multiplication of a fraction by a whole number. Create a frequency table and/or line plot to display measurement data. Solve problems involving addition and subtraction by using information presented in a data display. Analyze the data in a frequency table, line plot, bar graph or picture graph. J38: Writing to Explain J39: Make and Test Generalizations J40: Make and Test Conjectures Diagnostic Tests and Answer Keys, Grades 4-6 Grade 4 Diagnostic Test, Form A Grade 4 Diagnostic Test, Form B Grade 5 Diagnostic Test, Form A Grade 5 Diagnostic Test, Form B Grade 6 Diagnostic Test, Form A Grade 6 Diagnostic Test, Form B Grade 4: State-Specific Resources Minnesota Grade 4 MN-1: Fluency with Multiplication Facts Curriculum Standards: Demonstrate fluency with multiplication and division facts. Demonstrate fluency with multiplication and division facts with factors up to 12. MN-2: Fluency with Division Facts Curriculum Standards: Demonstrate fluency with multiplication and division facts. Demonstrate fluency with multiplication and division facts with factors up to 12. MN-3: Display Data in Timelines Curriculum Standards: Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. MN-4: Display Data in Venn Diagrams Curriculum Standards: Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. MN-5: Round Decimals to the Nearest Tenth Curriculum Standards: Round decimals to the nearest tenth. The student will round decimals to the nearest whole number. MN-6: Areas of Polygons Curriculum Standards: Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Find the area of polygons that can be decomposed into rectangles. MN-7: Congruent Figures and Motions Curriculum Standards: Apply translations (slides) to figures. Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Apply rotations (turns) of 90° clockwise or counterclockwise. Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent. Tennessee Grade 4 TN 1 Expanded Form and Place Value TN 2 Measure to Relate Customary Units TN 3 Measure to Relate Metric Units TN 4 Reflex Angles Credits, enVision Math National Grade 4 Teacher Resources Container Teaching Tools Intended Role: Instructor English Language Learners Toolkit Intended Role: Instructor Basic-Facts Timed Tests Intended Role: Instructor Assessment Sourcebook Intended Role: Instructor Today's Challenge Teacher's Guide Intended Role: Instructor Placement Test Intended Role: Instructor Placement Test: Answer Key Intended Role: Instructor End-of-Year Assessment Intended Role: Instructor End-of-Year Assessment: Answer Key Intended Role: Instructor Topics 1–4: Cumulative/Benchmark Assessment Intended Role: Instructor Topics 1–4: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–8: Cumulative/Benchmark Assessment Intended Role: Instructor Topics 1–8: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–12: Cumulative/Benchmark Assessment Intended Role: Instructor Topics 1–12: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–16: Cumulative/Benchmark Assessment Intended Role: Instructor Topics 1–16: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Math Practices Posters Intended Role: Instructor Math Practices and Problem Solving Handbook Intended Role: Instructor 3/4-Year Practice Performance Task 1 Intended Role: Instructor 3/4-Year Practice Performance Task 1: Answer Key Intended Role: Instructor 3/4-Year Practice Performance Task 2 Intended Role: Instructor 3/4-Year Practice Performance Task 2: Answer Key Intended Role: Instructor Next Generation Assessment Practice Test Intended Role: Instructor Next Generation Assessment Practice Test: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Intended Role: Instructor Online Teacher's Edition Program Overview: Grade 4 Intended Role: Instructor Professional Development Video Visual Learning 3–6 Intended Role: Instructor Online Placement Test: Answer Key Intended Role: Instructor Printable Online Placement Test Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 1 Assessment Intended Role: Instructor Topic 1 Assessment: Answer Key Intended Role: Instructor Topic 1 Performance Assessment Intended Role: Instructor Topic 1 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 1 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 1-1 Intended Role: Instructor Numbers Through One Million: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 1-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-1: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 1-2 Intended Role: Instructor Place Value Relationships: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 1-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-2: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 1-3 Intended Role: Instructor Compare Whole Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 1-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-3: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 1-4 Intended Role: Instructor Round Whole Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 1-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-4: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 1-5 Intended Role: Instructor Problem Solving: Construct Arguments: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 1-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-5: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 1 Online Assessment: Answer Key Intended Role: Instructor Topic 1 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 2 Assessment Intended Role: Instructor Topic 2 Assessment: Answer Key Intended Role: Instructor Topic 2 Performance Assessment Intended Role: Instructor Topic 2 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Fluency Practice/Assessment Master Intended Role: Instructor Fluency Practice/Assessment Master: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 2 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 2-1 Intended Role: Instructor Mental Math: Find Sums and Differences: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 2-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-1: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 2-2 Intended Role: Instructor Mental Math: Estimate Sums and Differences: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 2-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-2: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 2-4 Intended Role: Instructor Subtract Whole Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 2-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-4: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 2-5 Intended Role: Instructor Subtract Across Zeros: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 2-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-5: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 2-6 Intended Role: Instructor Problem Solving: Reasoning: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 2-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-6: Enrichment: Answer Key Intended Role: Instructor Topic 2 Online Assessment: Answer Key Intended Role: Instructor Topic 2 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 3 Assessment Intended Role: Instructor Topic 3 Assessment: Answer Key Intended Role: Instructor Topic 3 Performance Assessment Intended Role: Instructor Topic 3 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 3 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 3-1 Intended Role: Instructor Mental Math: Multiply by Multiples of 10, 100, and 1,000: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 3-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 3-2 Intended Role: Instructor Mental Math: Round to Estimate Products: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 3-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-2: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 3-3 Intended Role: Instructor The Distributive Property: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 3-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-3: Enrichment: Answer Key Intended Role: Instructor Topic 3 Online Assessment: Answer Key Intended Role: Instructor Topic 3 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 4 Assessment Intended Role: Instructor Topic 4 Assessment: Answer Key Intended Role: Instructor Topic 4 Performance Assessment Intended Role: Instructor Topic 4 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 4 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 4-1 Intended Role: Instructor Mental Math: Multiply Multiples of 10: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 4-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 4-3 Intended Role: Instructor Estimate: Use Rounding: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 4-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-3: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 4-4 Intended Role: Instructor Estimate: Use Compatible Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 4-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-4: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 4-9 Intended Role: Instructor Multiply 2-Digit by 2-Digit Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 4-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-9: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 4-10 Intended Role: Instructor Continue to Multiply by 2-Digit Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 4-10: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-10: Enrichment: Answer Key Intended Role: Instructor Topic 4 Online Assessment: Answer Key Intended Role: Instructor Topic 4 Online Assessment: Printable Intended Role: Instructor Topics 1–4: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–4: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 5 Assessment Intended Role: Instructor Topic 5 Assessment: Answer Key Intended Role: Instructor Topic 5 Performance Assessment Intended Role: Instructor Topic 5 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 5 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-1 Intended Role: Instructor Mental Math: Find Quotients: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-1: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-2 Intended Role: Instructor Mental Math: Estimate Quotients: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-2: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-3 Intended Role: Instructor Mental Math: Estimate Quotients for Greater Dividends: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-3: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-4 Intended Role: Instructor Interpret Remainders: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-4: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-5 Intended Role: Instructor Division as Sharing: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-5: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-6 Intended Role: Instructor Use Partial Quotients to Divide: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-6: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 5-7 Intended Role: Instructor Use Partial Quotients to Divide: Greater Dividends: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 5-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-7: Enrichment: Answer Key Intended Role: Instructor Topic 5 Online Assessment: Answer Key Intended Role: Instructor Topic 5 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 6 Assessment Intended Role: Instructor Topic 6 Assessment: Answer Key Intended Role: Instructor Topic 6 Performance Assessment Intended Role: Instructor Topic 6 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 6 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 6-1 Intended Role: Instructor Solve Comparison Situations: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 6-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-1: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 6-3 Intended Role: Instructor Solve Multi-Step Problems: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 6-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-3: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 6-4 Intended Role: Instructor Solve More Multi-Step Problems: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 6-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-4: Enrichment: Answer Key Intended Role: Instructor Topic 6 Online Assessment: Answer Key Intended Role: Instructor Topic 6 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 7 Assessment Intended Role: Instructor Topic 7 Assessment: Answer Key Intended Role: Instructor Topic 7 Performance Assessment Intended Role: Instructor Topic 7 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 7 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 7-1 Intended Role: Instructor Understand Factors: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 7-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-1: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 7-2 Intended Role: Instructor Factors: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 7-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-2: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 7-3 Intended Role: Instructor Problem Solving: Repeated Reasoning: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 7-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-3: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 7-4 Intended Role: Instructor Prime and Composite Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 7-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-4: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 7-5 Intended Role: Instructor Multiples: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 7-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-5: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 7 Online Assessment: Answer Key Intended Role: Instructor Topic 7 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 8 Assessment Intended Role: Instructor Topic 8 Assessment: Answer Key Intended Role: Instructor Topic 8 Performance Assessment Intended Role: Instructor Topic 8 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 8 Intended Role: Instructor Professional Development Video Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-1 Intended Role: Instructor Equivalent Fractions: Area Models: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-1: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-2 Intended Role: Instructor Equivalent Fractions: Number Lines: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-2: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-3 Intended Role: Instructor Generate Equivalent Fractions: Multiplication: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-3: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-4 Intended Role: Instructor Generate Equivalent Fractions: Division: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-4: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-5 Intended Role: Instructor Use Benchmarks to Compare Fractions: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-5: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-6 Intended Role: Instructor Compare Fractions: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-6: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 8-7 Intended Role: Instructor Problem Solving: Construct Arguments: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 8-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-7: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 8 Online Assessment: Answer Key Intended Role: Instructor Topic 8 Online Assessment: Printable Intended Role: Instructor Topics 1–8: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–8: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 9 Assessment Intended Role: Instructor Topic 9 Assessment: Answer Key Intended Role: Instructor Topic 9 Performance Assessment Intended Role: Instructor Topic 9 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 9 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-1 Intended Role: Instructor Model Addition of Fractions: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-2 Intended Role: Instructor Decompose Fractions: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-2: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-3 Intended Role: Instructor Add Fractions with Like Denominators: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-3: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-4 Intended Role: Instructor Model Subtraction of Fractions: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-4: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-5 Intended Role: Instructor Subtract Fractions with Like Denominators: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-5: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-6 Intended Role: Instructor Add and Subtract Fractions with Like Denominators: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-6: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-7 Intended Role: Instructor Estimate Fraction Sums and Differences: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-7: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-8 Intended Role: Instructor Model Addition and Subtraction of Mixed Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-8: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-9 Intended Role: Instructor Add Mixed Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-9: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-10 Intended Role: Instructor Subtract Mixed Numbers: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-10: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-10: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 9-11 Intended Role: Instructor Problem Solving: Model with Math: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 9-11: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-11: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 9 Online Assessment: Answer Key Intended Role: Instructor Topic 9 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 10 Assessment Intended Role: Instructor Topic 10 Assessment: Answer Key Intended Role: Instructor Topic 10 Performance Assessment Intended Role: Instructor Topic 10 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 10 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 10-1 Intended Role: Instructor Fractions as Multiples of Unit Fractions: Use Models: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 10-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-1: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 10-2 Intended Role: Instructor Multiply a Fraction by a Whole Number: Use Models: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 10-2: Quick Check: Answer Key Intended Role: Instructor 10-2: Printable Quick Check Intended Role: Instructor 10-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-2: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 10-3 Intended Role: Instructor Multiply a Fraction by a Whole Number: Use Symbols: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 10-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-3: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 10-4 Intended Role: Instructor Multiply a Whole Number and a Mixed Number: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 10-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-4: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 10-5 Intended Role: Instructor Solve Time Problems: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 10-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-5: Enrichment: Answer Key Intended Role: Instructor Topic 10 Online Assessment: Answer Key Intended Role: Instructor Topic 10 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 11 Assessment Intended Role: Instructor Topic 11 Assessment: Answer Key Intended Role: Instructor Topic 11 Performance Assessment Intended Role: Instructor Topic 11 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 11 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 11-1 Intended Role: Instructor Read Line Plots: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 11-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 11-2 Intended Role: Instructor Make Line Plots: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 11-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-2: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 11-3 Intended Role: Instructor Use Line Plots to Solve Problems: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 11-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-3: Enrichment: Answer Key Intended Role: Instructor Topic 11 Online Assessment: Answer Key Intended Role: Instructor Topic 11 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 12 Assessment Intended Role: Instructor Topic 12 Assessment: Answer Key Intended Role: Instructor Topic 12 Performance Assessment Intended Role: Instructor Topic 12 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 12 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 12-1 Intended Role: Instructor Fractions and Decimals: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 12-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 12-2 Intended Role: Instructor Fractions and Decimals on the Number Line: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 12-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-2: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 12-3 Intended Role: Instructor Compare Decimals: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 12-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-3: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 12-4 Intended Role: Instructor Add Fractions with Denominators of 10 and 100: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 12-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-4: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 12-5 Intended Role: Instructor Solve Word Problems Involving Money: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 12-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-5: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 12-6 Intended Role: Instructor Problem Solving: Look For & Use Structure: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 12-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-6: Enrichment: Answer Key Intended Role: Instructor Topic 12 Online Assessment: Answer Key Intended Role: Instructor Topic 12 Online Assessment: Printable Intended Role: Instructor Topics 1–12: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–12: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 13 Assessment Intended Role: Instructor Topic 13 Assessment: Answer Key Intended Role: Instructor Topic 13 Performance Assessment Intended Role: Instructor Topic 13 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 13 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-1 Intended Role: Instructor Equivalence with Customary Units of Length: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-2 Intended Role: Instructor Equivalence with Customary Units of Capacity: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-2: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-3 Intended Role: Instructor Equivalence with Customary Units of Weight: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-3: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-4 Intended Role: Instructor Equivalence with Metric Units of Length: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-4: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-5 Intended Role: Instructor Equivalence with Metric Units of Capacity and Mass: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-5: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-6 Intended Role: Instructor Solve Perimeter and Area Problems: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-6: Enrichment: Answer Key Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 13-7 Intended Role: Instructor Problem Solving: Precision: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 13-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-7: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 13 Online Assessment: Answer Key Intended Role: Instructor Topic 13 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 14 Assessment Intended Role: Instructor Topic 14 Assessment: Answer Key Intended Role: Instructor Topic 14 Performance Assessment Intended Role: Instructor Topic 14 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 14 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 14-1 Intended Role: Instructor Number Sequences: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 14-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-1: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 14-2 Intended Role: Instructor Patterns: Number Rules: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 14-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-2: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 14-3 Intended Role: Instructor Patterns: Repeating Shapes: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 14-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-3: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 14-4 Intended Role: Instructor Problem Solving: Look For & Use Structure: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 14-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-4: Enrichment: Answer Key Intended Role: Instructor Topic 14 Online Assessment: Answer Key Intended Role: Instructor Topic 14 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 15 Assessment Intended Role: Instructor Topic 15 Assessment: Answer Key Intended Role: Instructor Topic 15 Performance Assessment Intended Role: Instructor Topic 15 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 15 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 15-1 Intended Role: Instructor Lines, Rays, and Angles: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 15-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 15-2 Intended Role: Instructor Understand Angles and Unit Angles: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 15-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-2: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 15-3 Intended Role: Instructor Measure with Unit Angles: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 15-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-3: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 15-4 Intended Role: Instructor Measure and Draw Angles: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 15-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-4: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 15-5 Intended Role: Instructor Add and Subtract Angle Measures: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 15-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-5: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 15-6 Intended Role: Instructor Problem Solving: Use Appropriate Tools: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 15-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-6: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 15 Online Assessment: Answer Key Intended Role: Instructor Topic 15 Online Assessment: Printable Intended Role: Instructor Home-School Connection Intended Role: Instructor Topic 16 Assessment Intended Role: Instructor Topic 16 Assessment: Answer Key Intended Role: Instructor Topic 16 Performance Assessment Intended Role: Instructor Topic 16 Performance Assessment: Answer Key Intended Role: Instructor Problem-Solving Reading Activity Guide Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 16 Intended Role: Instructor Professional Development Video Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 16-1 Intended Role: Instructor Lines: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 16-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-1: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 16-2 Intended Role: Instructor Classify Triangles: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 16-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-2: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 16-3 Intended Role: Instructor Classify Quadrilaterals: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 16-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-3: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 16-4 Intended Role: Instructor Line Symmetry: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 16-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-4: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 16-5 Intended Role: Instructor Draw Shapes with Line Symmetry: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 16-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-5: Enrichment: Answer Key Intended Role: Instructor Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 16-6 Intended Role: Instructor Problem Solving: Critique Reasoning: Listen & Look Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor 16-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-6: Enrichment: Answer Key Intended Role: Instructor Problem-Solving Reading Mats Intended Role: Instructor Topic 16 Online Assessment: Answer Key Intended Role: Instructor Topic 16 Online Assessment: Printable Intended Role: Instructor Topics 1–16: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–16: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Online End-of-Year Assessment: Answer Key Intended Role: Instructor Printable Online End-of-Year Assessment Intended Role: Instructor Teacher's Edition eText: Grade 4 Topic 17 Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-1 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-2 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-3 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-4 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-5 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-7 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-8 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-9 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Teacher's Edition eText: Grade 4 Lesson 17-10 Intended Role: Instructor Solve & Share Solution Intended Role: Instructor Online 3/4-Year Practice Performance Task 1: Answer Key Intended Role: Instructor Printable Online 3/4-Year Practice Performance Task 1 Intended Role: Instructor Online 3/4-Year Practice Performance Task 2: Answer Key Intended Role: Instructor Printable Online 3/4-Year Practice Performance Task 2 Intended Role: Instructor Online Next Generation Assessment Practice Test: Answer Key Intended Role: Instructor Printable Online Next Generation Assessment Practice Test Intended Role: Instructor Booklet A: Numbers, Place Value, Money, and Patterns in Grades K-3 Intended Role: Instructor Booklet B: Basic Facts in Grades K-3 Intended Role: Instructor Booklet C: Computation with Whole numbers in Grades K-3 Intended Role: Instructor Booklet D: Measurement, Geometry, Data, and Probability in Grades K-3 Intended Role: Instructor Booklet E: Problem Solving in Grades K-3 Intended Role: Instructor Teacher's Guide, Grades K-3 Intended Role: Instructor Booklet F: Numeration, Patterns, and Relationships in Grades 4-6 Intended Role: Instructor Booklet G: Operations with Whole Numbers in Grades 4-6 Intended Role: Instructor Booklet H: Fractions, Decimals, and Percents in Grades 4-6 Intended Role: Instructor Booklet I: Measurement, Geometry, Data, and Probability in Grades 4-6 Intended Role: Instructor Booklet J: Problem Solving in Grades 4-6 Intended Role: Instructor Teacher's Guide, Grades 4-6 Intended Role: Instructor Diagnostic Tests and Answer Keys, Grades 4-6 Intended Role: Instructor MN-1: Fluency with Multiplication Facts Teacher's Guide Intended Role: Instructor MN-2: Fluency with Division Facts Teacher's Guide Intended Role: Instructor MN-3: Display Data in Timelines Teacher's Guide Intended Role: Instructor MN-4: Display Data in Venn Diagrams Teacher's Guide Intended Role: Instructor MN-5: Round Decimals to the Nearest Tenth Teacher's Guide Intended Role: Instructor MN-6: Areas of Polygons Teacher's Guide Intended Role: Instructor MN-7: Congruent Figures and Motions Teacher's Guide Intended Role: Instructor TN 1 Expanded Form and Place Value Teacher's Guide Intended Role: Instructor TN 2 Measure to Relate Customary Units Teacher's Guide Intended Role: Instructor TN 3 Measure to Relate Metric Units Teacher's Guide Intended Role: Instructor TN 4 Reflex Angles Teacher's Guide Intended Role: Instructor Teacher's Edition eText: Grade 4 Intended Role: Instructor eText Container Student's Edition eText: Grade 4 Interactive Student Edition: Grade 4 Tools Math Tool - Counters: Arrays Math Tool - Fractions: Fraction Strips Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Place Value Blocks: Arrays Math Tool - Geometry: Shapes Grade 4: Game Center Math Tool - Bar Diagrams: Compare: Multiplication and Division Grade 4: Accessible Student Edition Math Tool - Bar Diagrams: Equal Groups: Multiplication and Division Grade 4: Glossary Math Tool - Number Line: Add & Subtract Fractions Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Place Value Blocks: Place-Value Blocks Grade 4: ACTIVe-book Vol. 1 Math Tool - Fractions: Pieces Math Tool - Money Math Tool - Fractions: Denominators Math Tool - Geometry: Tangrams Math Tool - Fractions: Equivalent Shapes Math Tool - Fractions: Fraction Strips Math Tool - Place Value Blocks: Arrays Math Tools Math Tool - I/O Machine: Explore Math Tool - Geometry: Shapes Math Tool - Fractions: Pieces Math Tool - Money Math Tool - Place Value Blocks: Arrays Math Tool - Data and Graphs: Create Plots Math Tool - Fractions: Fraction Strips Math Tool - Number Line: Numbers Math Tool - Place Value Blocks: Place-Value Chips Math Tool - Bar Diagrams: Put Together/Take Apart