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Curriculum Standards:


Compare benchmark fractions (¼, ⅓, ½, ⅔, 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
Read and write numbers to 1000 using base-ten numerals, number names and expanded form. - M.2.7
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
Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. - 1.3.1.1
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
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
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
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
Count within 1000 and skip-count by 5s, 10s and 100s. - M.2.6
Use fraction models to add 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
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
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
Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. - NC.3.G.1.a
Demonstrate the ability to measure length or distance using objects. - 1.GM.B.7
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
Make sense of problems and persevere in solving them. - 5.OA.9
Justify the reasonableness of a product when multiplying with fractions. - 5.NF.B.5
Interpret numerical expressions without evaluating them. - 5.OA.4
Estimate results of sums, differences and products with fractions and decimals to the thousandths. - 5.NF.B.4
Compare the lengths of two objects indirectly by using a third object. - 1.GM.B.6
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
Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.OA.5
Understand two-digit numbers are composed of ten(s) and one(s). - 1.NBT.A.2
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
Compare two two-digit numbers using the symbols >, = or <. - 1.NBT.A.3
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
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, ⅓, ½, ⅔, 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
Convert metric units of mass. - 5.MD.12
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
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
Critique the reasoning of others using understanding of line plots and fractions. - 5.MD.18
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
Solve problems using data in a line plot. - 5.MD.17
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
Be precise when solving measurement problems. - 5.MD.14
Define a first quadrant Cartesian coordinate system. - 5.GM.C.6
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. - M.2.14
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
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
Organize and display data in a line plot. - 5.MD.16
Estimate lengths using units of inches, feet, centimeters, and meters. - M.2.16
Read and analyze line plots. - 5.MD.15
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
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
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
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
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
Understand that attributes belonging to a category of figures also belong to all subcategories. - 5.GM.A.1
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
Use estimation strategies to assess reasonableness of answers. - NC.3.NBT.2.a
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
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
Model problems using equations, drawings, arrays, and bar diagrams. - 2.OA.15
The student will sort and classify concrete objects according to one or two attributes. - 1.13
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
Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. - 2.N.3.1
100 can be thought of as a bundle of ten tens – called a “hundred.” - M.2.5a
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
The student will count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110. - 1.1d
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
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
Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole. - 2.GM.A.3
Solve problems using information presented in line plots, picture graphs and bar graphs. - 2.DS.A.4
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
The student will write the numerals 0 to 110 in sequence and out-of-sequence. - 1.1b
Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. - M.4.24
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
The student will count forward orally by ones to 110, starting at any number between 0 and 110. - 1.1a
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
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
Describe the shares using the words halves, thirds, half of, a third of, fourths, fourth of, quarter of. - NC.2.G.3.a
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 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
Make sense of problems and persevere in solving them. - 5.MP.1
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
Look for and make use of structure. - 5.MP.7
Attend to precision. - 5.MP.6
Look for and express regularity in repeated reasoning. - 5.MP.8
Construct viable arguments and critique the reasoning of others. - 5.MP.3
Reason abstractly and quantitatively. - 5.MP.2
Use appropriate tools strategically. - 5.MP.5
Model with mathematics. - 5.MP.4
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
Recognize and combine groups with totals up to 5 (conceptual subitizing). - NC.K.OA.6
Compose and decompose larger shapes using smaller two-dimensional shapes. - 1.GM.1.2
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
The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. - 3.1b
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
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
The student will demonstrate fluency with addition and subtraction within 10. - 1.7b
Represent addition and subtraction, within 10: - NC.K.OA.1
Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. - 5.2.1.1
Find the measure of an angle that turns through a fraction of a circle. - 4.MD.13
Add to/Take from- Change Unknown - NC.2.OA.1.b.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.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
Understand that the two digits of a two-digit number represent amounts of tens and ones. - NC.1.NBT.2
Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. - NC.2.MD.3
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
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
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
Write equations to show the parts of 10. - K.OA.25
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
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
Find number partners for 10. - K.OA.27
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
One-Step problems: - NC.2.OA.1.a
Unitize by making a ten from a collection of ten ones. - NC.1.NBT.2.a
Two-Step problems involving single digits: - NC.2.OA.1.b
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
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
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 compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ≠), with models. - 3.2c
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 each successive number name refers to a quantity that is one larger. - M.K.4c
Estimate the length of an object by relating the length of the object to a measurement I know. - 2.MD.8
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 with coins. - 2.MD.1
Solve problems involving addition and subtraction of minutes. - 3.GM.B.6
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
The student will investigate the passage of time and tell time to the hour and half-hour, using analog and digital clocks. - 1.9a
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 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 addition and subtraction to solve problems with unknown angle measures. - 4.MD.16
The student will estimate and determine the sum or difference of two whole numbers. - 3.3a
Use a protractor to measure and draw angles. - 4.MD.15
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
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
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, 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
Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. - NC.4.G.3
Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. - NC.4.G.1
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
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
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
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 demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. - 3.4c
Solve word problems involving multiplication of a fraction by a whole number. - NC.4.NF.4.b
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
Tell time to the quarter-hour and distinguish between a.m. and p.m. - 2.3.3.1
Add and subtract within 20. - 1.RA.C.7
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
Describe the numerator as representing the number of pieces being considered. - 3.NF.A.2a
Express the length of an object as a whole number of non-standard length units. - NC.1.MD.2.a
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
Use previously learned knowledge about volumes to choose the appropriate tools to solve volume problems. - 5.MD.6
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
Find the volume of solid figures. - 5.MD.1
Demonstrate fluency with addition and subtraction within 1000. - 3.NBT.A.3
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
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. - NC.5.NF.4
Use words or mathematical symbols to express a rule for a given pattern. - 4.RA.C.7
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 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
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
Given a number from 1–20, count out that many objects. - NC.K.CC.5.a
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
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
Comparing common numerator or common denominators. - NC.4.NF.2.c
Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. - NC.K.CC.5.c
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
Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. - 3.N.2.3
Recognize that a number can be used to represent how many objects are in a set up to 10. - K.N.1.2
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
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 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
Demonstrate fluency of multiplication facts with factors up to 10. - 3.N.2.2
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
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
Demonstrate understanding of addition and subtraction by making connections among representations. - NC.K.OA.1.b
Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line. - 3.NF.A.4
Measure the lengths of objects and make a line plot to organize the data. - 2.MD.22
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
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. - 1.RA.A.4
Add and subtract on a number line. - 2.MD.20
Explain why fraction comparisons are only valid when the two fractions refer to the same whole. - 3.NF.A.7
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
Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. - 1.RA.A.3
Identify quadrilaterals and use attributes to describe them. - 3.G.1
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
Add or subtract to solve problems about measurements. - 2.MD.18
The student will tell how many are in a given set of 20 or fewer objects by counting orally. - K.1a
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
Demonstrate that a number can be used to represent “how many” are in a set. - K.NS.B.9
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
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
Explaining that a fraction with the same numerator and denominator equals one whole. - NC.3.NF.3.b
The student will recognize and describe with fluency part-whole relationships for numbers up to 5. - K.4a
Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. - NC.3.NF.3.a
The student will investigate and describe part-whole relationships for numbers up to 10. - K.4b
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
Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. - 5.NBT.A.1
Classify two-dimensional shapes by their sides and/or angles. - 4.GM.A.2
Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. - 1.1.1.1
Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. - 5.NBT.A.2
Ask and answer questions about the total number of data points. - NC.1.MD.4.a
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
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
Ask and answer questions about how many more or less are in one category than in another. - NC.1.MD.4.c
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
Tell time to the half hour. - 1.MD.13
The student will count forward orally by ones from 0 to 100. - K.3a
The student will count forward by tens to determine the total number of objects to 100. - K.3d
Tell time to the hour. - 1.MD.11
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
Understand the whole is the interval from 0 to 1. - 3.NF.A.3a
Count to the numbers 8 and 9. - K.NCC.20
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
The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. - 5.6a
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 practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. - 5.6b
Round numbers from billions to thousandths place. - 5.NBT.A.5
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
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
Use data to create picture and bar-type graphs to demonstrate one-to-one correspondence. - 1.D.1.2
Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. - 4.NF.B.4
Draw conclusions from picture and bar-type graphs. - 1.D.1.3
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
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
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
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
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
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
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
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
Determining whether objects can be placed into two equal groups. - NC.2.OA.3.b
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
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
Know relative sizes of measurement units within one system of units. - 4.GM.C.6
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
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
Draw cubes and describe how they look. - 1.G.4
Divide rectangles into equal squares. - 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
Make equal shares that do not have the same shape. - 1.G.7
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
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
Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. - 5.1.3.1
Measure angles in geometric figures and real-world objects with a protractor or angle ruler. - 4.GM.2.1
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
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
Represent a problem situation with a mathematical model. - 5.NC.60
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
Use models to multiply two fractions. - 5.NC.64
Multiply fractions and whole numbers. - 5.NC.63
Multiply a fraction by a whole number. - 5.NC.62
Subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.58
Use models to subtract mixed numbers. - 5.NC.57
Locate points on a coordinate grid. - 5.G.1
Graph points on a coordinate grid. - 5.G.2
Add mixed numbers using equivalent fractions and a common denominator. - 5.NC.56
Add mixed numbers using models. - 5.NC.55
Solve real-world problems by graphing points. - 5.G.3
Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.G.4
Classify triangles by their angles and sides. - 5.G.5
Classify quadrilaterals by their properties. - 5.G.6
Classify quadrilaterals using a hierarchy. - 5.G.7
Add and subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.59
Construct arguments about geometric figures. - 5.G.8
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
Use previously learned knowledge to make sense of problems and persevere in solving them. - 5.NC.69
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
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
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
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
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
Tell time to the hour and half-hour. - 1.3.2.2
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 technology, and the context of the problem to assess the reasonableness of results. - 4.1.1.5
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
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
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
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
Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. - 5.NC.77
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
Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. - 4.N.1.2
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
Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use 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
Represent data using line plots and interpret data in line plots to solve problems. - 4.MD.2
Recognize and use the relationship between inches, feet, and yards to measure and compare objects. - 5.GM.3.3
Solve problems involving line plots and fractions. - 4.MD.3
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
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
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
Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. - 5.NC.21
Use models and strategies to solve word problems. - 5.NC.20
Compare two numbers, within 10, presented as written numerals. - NC.K.CC.7
Use prior math knowledge and equations or bar diagrams to solve problems. - 5.NC.14
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
Understand that rectangles can have equal perimeters but different areas, or rectangles can have equal areas but different perimeters. - 3.GM.D.16
Create growth patterns involving geometric shapes and define the single operation rule of the pattern. - 4.A.1.3
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 the strategy of making a ten to add quickly and accurately. - 2.OA.3
Use place-value patterns and mental math to find quotients. - 5.NC.32
Use previously learned concepts and skills to represent and solve problems. - 5.NC.31
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 quan
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